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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 17160l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17160.c2 | 17160l1 | \([0, -1, 0, -1538696, 8952029820]\) | \(-393443624385770851876/33577011001321734375\) | \(-34382859265353456000000\) | \([2]\) | \(1198080\) | \(3.0039\) | \(\Gamma_0(N)\)-optimal |
| 17160.c1 | 17160l2 | \([0, -1, 0, -74743696, 246985407820]\) | \(22548490527122525577915938/183925440576065170125\) | \(376679302299781468416000\) | \([2]\) | \(2396160\) | \(3.3505\) |
Rank
sage: E.rank()
The elliptic curves in class 17160l have rank \(0\).
Complex multiplication
The elliptic curves in class 17160l do not have complex multiplication.Modular form 17160.2.a.l
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.
