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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 238260v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 238260.v1 | 238260v1 | \([0, 1, 0, -110225, -10656252]\) | \(196755275776/49141125\) | \(36990200303298000\) | \([2]\) | \(2903040\) | \(1.8892\) | \(\Gamma_0(N)\)-optimal |
| 238260.v2 | 238260v2 | \([0, 1, 0, 267020, -67393900]\) | \(174820311344/264515625\) | \(-3185758877796000000\) | \([2]\) | \(5806080\) | \(2.2358\) |
Rank
sage: E.rank()
The elliptic curves in class 238260v have rank \(1\).
Complex multiplication
The elliptic curves in class 238260v do not have complex multiplication.Modular form 238260.2.a.v
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.
