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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 17424t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17424.bu5 | 17424t1 | \([0, 0, 0, 726, -9317]\) | \(2048/3\) | \(-61990462512\) | \([2]\) | \(10240\) | \(0.75633\) | \(\Gamma_0(N)\)-optimal |
| 17424.bu4 | 17424t2 | \([0, 0, 0, -4719, -93170]\) | \(35152/9\) | \(2975542200576\) | \([2, 2]\) | \(20480\) | \(1.1029\) | |
| 17424.bu2 | 17424t3 | \([0, 0, 0, -70059, -7136822]\) | \(28756228/3\) | \(3967389600768\) | \([2]\) | \(40960\) | \(1.4495\) | |
| 17424.bu3 | 17424t4 | \([0, 0, 0, -26499, 1583890]\) | \(1556068/81\) | \(107119519220736\) | \([2, 2]\) | \(40960\) | \(1.4495\) | |
| 17424.bu1 | 17424t5 | \([0, 0, 0, -418539, 104219962]\) | \(3065617154/9\) | \(23804337604608\) | \([2]\) | \(81920\) | \(1.7960\) | |
| 17424.bu6 | 17424t6 | \([0, 0, 0, 17061, 6279658]\) | \(207646/6561\) | \(-17353362113759232\) | \([2]\) | \(81920\) | \(1.7960\) |
Rank
sage: E.rank()
The elliptic curves in class 17424t have rank \(1\).
Complex multiplication
The elliptic curves in class 17424t do not have complex multiplication.Modular form 17424.2.a.t
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
