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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 35594c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35594.a2 | 35594c1 | \([1, -1, 0, -3679, 132301]\) | \(-2146689/1664\) | \(-4269368744576\) | \([]\) | \(103320\) | \(1.1223\) | \(\Gamma_0(N)\)-optimal |
35594.a1 | 35594c2 | \([1, -1, 0, -291169, -66277889]\) | \(-1064019559329/125497034\) | \(-321991054384970906\) | \([]\) | \(723240\) | \(2.0953\) |
Rank
sage: E.rank()
The elliptic curves in class 35594c have rank \(0\).
Complex multiplication
The elliptic curves in class 35594c do not have complex multiplication.Modular form 35594.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.