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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 115920.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115920.t1 | 115920cb1 | \([0, 0, 0, -709430643, -3040869636558]\) | \(489781415227546051766883/233890092903563264000\) | \(18856586029550943130877952000\) | \([2]\) | \(74317824\) | \(4.1194\) | \(\Gamma_0(N)\)-optimal |
115920.t2 | 115920cb2 | \([0, 0, 0, 2546397837, -23128680192462]\) | \(22649115256119592694355357/15973509811739648000000\) | \(-1287809407485835229528064000000\) | \([2]\) | \(148635648\) | \(4.4660\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.t have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.t do not have complex multiplication.Modular form 115920.2.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 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.