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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)
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.