Properties

Label 248430hi
Number of curves $8$
Conductor $248430$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("hi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 248430hi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.hi7 248430hi1 \([1, 1, 1, -4119970, -3219245905]\) \(13619385906841/6048000\) \(3434473236343968000\) \([2]\) \(10616832\) \(2.5152\) \(\Gamma_0(N)\)-optimal
248430.hi6 248430hi2 \([1, 1, 1, -4782450, -2115289233]\) \(21302308926361/8930250000\) \(5071214388039140250000\) \([2, 2]\) \(21233664\) \(2.8618\)  
248430.hi5 248430hi3 \([1, 1, 1, -12193945, 12450724775]\) \(353108405631241/86318776320\) \(49017778945932782469120\) \([2]\) \(31850496\) \(3.0645\)  
248430.hi4 248430hi4 \([1, 1, 1, -36084630, 81949845375]\) \(9150443179640281/184570312500\) \(104811805308348632812500\) \([2]\) \(42467328\) \(3.2084\)  
248430.hi8 248430hi5 \([1, 1, 1, 15920050, -15513947233]\) \(785793873833639/637994920500\) \(-362297698310292257740500\) \([2]\) \(42467328\) \(3.2084\)  
248430.hi2 248430hi6 \([1, 1, 1, -181788825, 943255264167]\) \(1169975873419524361/108425318400\) \(61571404462115274854400\) \([2, 2]\) \(63700992\) \(3.4111\)  
248430.hi1 248430hi7 \([1, 1, 1, -2908556505, 60374792910375]\) \(4791901410190533590281/41160000\) \(23373498414007560000\) \([2]\) \(127401984\) \(3.7577\)  
248430.hi3 248430hi8 \([1, 1, 1, -168539225, 1086600036647]\) \(-932348627918877961/358766164249920\) \(-203732273350220624194086720\) \([2]\) \(127401984\) \(3.7577\)  

Rank

sage: E.rank()
 

The elliptic curves in class 248430hi have rank \(0\).

Complex multiplication

The elliptic curves in class 248430hi do not have complex multiplication.

Modular form 248430.2.a.hi

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - q^{12} - q^{15} + q^{16} + 6q^{17} + q^{18} + 8q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.