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SageMath
E = EllipticCurve("go1")
E.isogeny_class()
Elliptic curves in class 348480.go
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.go1 | 348480go1 | \([0, 0, 0, -165528, -25012152]\) | \(379275264/15125\) | \(20002255903872000\) | \([2]\) | \(2949120\) | \(1.8944\) | \(\Gamma_0(N)\)-optimal |
| 348480.go2 | 348480go2 | \([0, 0, 0, 74052, -91423728]\) | \(2122416/171875\) | \(-3636773800704000000\) | \([2]\) | \(5898240\) | \(2.2410\) |
Rank
sage: E.rank()
The elliptic curves in class 348480.go have rank \(1\).
Complex multiplication
The elliptic curves in class 348480.go do not have complex multiplication.Modular form 348480.2.a.go
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
