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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 32064.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32064.c1 | 32064b2 | \([0, -1, 0, -929, -7551]\) | \(2708870984/753003\) | \(24674402304\) | \([2]\) | \(21504\) | \(0.70138\) | |
32064.c2 | 32064b1 | \([0, -1, 0, 151, -855]\) | \(92345408/121743\) | \(-498659328\) | \([2]\) | \(10752\) | \(0.35480\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32064.c have rank \(1\).
Complex multiplication
The elliptic curves in class 32064.c do not have complex multiplication.Modular form 32064.2.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 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.