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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 77616.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77616.di1 | 77616dc4 | \([0, 0, 0, -7230195, -7482943566]\) | \(4406910829875/7744\) | \(73452202834526208\) | \([2]\) | \(1658880\) | \(2.4955\) | |
| 77616.di2 | 77616dc3 | \([0, 0, 0, -456435, -114447438]\) | \(1108717875/45056\) | \(427358271037243392\) | \([2]\) | \(829440\) | \(2.1489\) | |
| 77616.di3 | 77616dc2 | \([0, 0, 0, -115395, -3770942]\) | \(13060888875/7086244\) | \(92199391435210752\) | \([2]\) | \(552960\) | \(1.9462\) | |
| 77616.di4 | 77616dc1 | \([0, 0, 0, -68355, 6831874]\) | \(2714704875/21296\) | \(277083069677568\) | \([2]\) | \(276480\) | \(1.5996\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 77616.di have rank \(1\).
Complex multiplication
The elliptic curves in class 77616.di do not have complex multiplication.Modular form 77616.2.a.di
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
