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SageMath
E = EllipticCurve("fw1")
E.isogeny_class()
Elliptic curves in class 121275fw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121275.bg2 | 121275fw1 | \([1, -1, 1, 628195, 1096404572]\) | \(163667323/3195731\) | \(-535323147713771484375\) | \([2]\) | \(3870720\) | \(2.6578\) | \(\Gamma_0(N)\)-optimal |
| 121275.bg1 | 121275fw2 | \([1, -1, 1, -12877430, 16816952072]\) | \(1409825840597/86806489\) | \(14541124685857751953125\) | \([2]\) | \(7741440\) | \(3.0044\) |
Rank
sage: E.rank()
The elliptic curves in class 121275fw have rank \(0\).
Complex multiplication
The elliptic curves in class 121275fw do not have complex multiplication.Modular form 121275.2.a.fw
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.
