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SageMath
E = EllipticCurve("ip1")
E.isogeny_class()
Elliptic curves in class 463680.ip
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 463680.ip1 | 463680ip1 | \([0, 0, 0, -2837722572, -24326957092464]\) | \(489781415227546051766883/233890092903563264000\) | \(1206821505891260360376188928000\) | \([2]\) | \(594542592\) | \(4.4660\) | \(\Gamma_0(N)\)-optimal |
| 463680.ip2 | 463680ip2 | \([0, 0, 0, 10185591348, -185029441539696]\) | \(22649115256119592694355357/15973509811739648000000\) | \(-82419802079093454689796096000000\) | \([2]\) | \(1189085184\) | \(4.8126\) |
Rank
sage: E.rank()
The elliptic curves in class 463680.ip have rank \(0\).
Complex multiplication
The elliptic curves in class 463680.ip do not have complex multiplication.Modular form 463680.2.a.ip
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.
