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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 337896f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 337896.f3 | 337896f1 | \([0, 0, 0, -23826, 816221]\) | \(2725888/1053\) | \(577826543251152\) | \([2]\) | \(884736\) | \(1.5315\) | \(\Gamma_0(N)\)-optimal |
| 337896.f2 | 337896f2 | \([0, 0, 0, -170031, -26407150]\) | \(61918288/1521\) | \(13354213444026624\) | \([2, 2]\) | \(1769472\) | \(1.8781\) | |
| 337896.f4 | 337896f3 | \([0, 0, 0, 24909, -83446594]\) | \(48668/85683\) | \(-3009149429387332608\) | \([2]\) | \(3538944\) | \(2.2247\) | |
| 337896.f1 | 337896f4 | \([0, 0, 0, -2704251, -1711663450]\) | \(62275269892/39\) | \(1369662917336064\) | \([2]\) | \(3538944\) | \(2.2247\) |
Rank
sage: E.rank()
The elliptic curves in class 337896f have rank \(2\).
Complex multiplication
The elliptic curves in class 337896f do not have complex multiplication.Modular form 337896.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
