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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 317889t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
317889.t2 | 317889t1 | \([0, 0, 1, -552630, 170463582]\) | \(-5304438784000/497763387\) | \(-1751501812460478507\) | \([]\) | \(3369600\) | \(2.2426\) | \(\Gamma_0(N)\)-optimal |
317889.t1 | 317889t2 | \([0, 0, 1, -45726330, 119013885279]\) | \(-3004935183806464000/2037123\) | \(-7168113846639603\) | \([]\) | \(10108800\) | \(2.7920\) |
Rank
sage: E.rank()
The elliptic curves in class 317889t have rank \(1\).
Complex multiplication
The elliptic curves in class 317889t do not have complex multiplication.Modular form 317889.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.