Properties

Label 46800el
Number of curves $2$
Conductor $46800$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("el1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800el

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.j1 46800el1 \([0, 0, 0, -3027675, -2027461750]\) \(65787589563409/10400000\) \(485222400000000000\) \([2]\) \(1105920\) \(2.4041\) \(\Gamma_0(N)\)-optimal
46800.j2 46800el2 \([0, 0, 0, -2739675, -2428645750]\) \(-48743122863889/26406250000\) \(-1232010000000000000000\) \([2]\) \(2211840\) \(2.7507\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46800el have rank \(0\).

Complex multiplication

The elliptic curves in class 46800el do not have complex multiplication.

Modular form 46800.2.a.el

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - 2q^{11} + q^{13} + 2q^{17} - 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.