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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 328560.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 328560.g1 | 328560g2 | \([0, -1, 0, -3286056, 2266271856]\) | \(511189448451769/7077888000\) | \(54333856366460928000\) | \([]\) | \(14370048\) | \(2.5924\) | |
| 328560.g2 | 328560g1 | \([0, -1, 0, -329016, -70972560]\) | \(513108539209/12597120\) | \(96702591042846720\) | \([]\) | \(4790016\) | \(2.0431\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 328560.g have rank \(0\).
Complex multiplication
The elliptic curves in class 328560.g do not have complex multiplication.Modular form 328560.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
