Properties

Label 248430.in
Number of curves $4$
Conductor $248430$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("in1")
 
E.isogeny_class()
 

Elliptic curves in class 248430.in

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.in1 248430in3 \([1, 0, 0, -4004036, 3082981446]\) \(12501706118329/2570490\) \(1459702233678870090\) \([2]\) \(8257536\) \(2.4825\)  
248430.in2 248430in2 \([1, 0, 0, -277586, 36981216]\) \(4165509529/1368900\) \(777356219118924900\) \([2, 2]\) \(4128768\) \(2.1359\)  
248430.in3 248430in1 \([1, 0, 0, -111966, -13996620]\) \(273359449/9360\) \(5315256199103760\) \([2]\) \(2064384\) \(1.7893\) \(\Gamma_0(N)\)-optimal
248430.in4 248430in4 \([1, 0, 0, 798944, 254224970]\) \(99317171591/106616250\) \(-60544090142916266250\) \([2]\) \(8257536\) \(2.4825\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 248430.2.a.in

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} + q^{12} - q^{15} + q^{16} + 6 q^{17} + q^{18} + O(q^{20})\) Copy content 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.