Properties

Label 7616d
Number of curves $2$
Conductor $7616$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 7616d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7616.a2 7616d1 \([0, 1, 0, 2015, -6081]\) \(3449795831/2071552\) \(-543044927488\) \([2]\) \(15360\) \(0.94098\) \(\Gamma_0(N)\)-optimal
7616.a1 7616d2 \([0, 1, 0, -8225, -57281]\) \(234770924809/130960928\) \(34330621509632\) \([2]\) \(30720\) \(1.2876\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7616d have rank \(0\).

Complex multiplication

The elliptic curves in class 7616d do not have complex multiplication.

Modular form 7616.2.a.d

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 4 q^{5} + q^{7} + q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} - q^{17} + 6 q^{19} + O(q^{20})\) 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 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.