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SageMath
E = EllipticCurve("gw1")
E.isogeny_class()
Elliptic curves in class 418950gw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 418950.gw1 | 418950gw1 | \([1, -1, 0, -28798632, 59707965456]\) | \(-1231922871794037145/5186378855952\) | \(-11120389912785520054800\) | \([]\) | \(39813120\) | \(3.0850\) | \(\Gamma_0(N)\)-optimal |
| 418950.gw2 | 418950gw2 | \([1, -1, 0, 67350393, 314773230141]\) | \(15757536948921630455/29083977048526848\) | \(-62360497367629412932915200\) | \([]\) | \(119439360\) | \(3.6343\) |
Rank
sage: E.rank()
The elliptic curves in class 418950gw have rank \(1\).
Complex multiplication
The elliptic curves in class 418950gw do not have complex multiplication.Modular form 418950.2.a.gw
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
