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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 10608c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10608.k2 | 10608c1 | \([0, -1, 0, -443, -12810]\) | \(-602275072000/4184843403\) | \(-66957494448\) | \([2]\) | \(9216\) | \(0.76053\) | \(\Gamma_0(N)\)-optimal |
10608.k1 | 10608c2 | \([0, -1, 0, -11428, -465392]\) | \(644811009586000/1651460733\) | \(422773947648\) | \([2]\) | \(18432\) | \(1.1071\) |
Rank
sage: E.rank()
The elliptic curves in class 10608c have rank \(0\).
Complex multiplication
The elliptic curves in class 10608c do not have complex multiplication.Modular form 10608.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.