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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 8624s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8624.bc2 | 8624s1 | \([0, -1, 0, 2728, 207152]\) | \(4657463/41503\) | \(-19999893286912\) | \([2]\) | \(18432\) | \(1.2335\) | \(\Gamma_0(N)\)-optimal |
8624.bc1 | 8624s2 | \([0, -1, 0, -40392, 2897840]\) | \(15124197817/1294139\) | \(623633036128256\) | \([2]\) | \(36864\) | \(1.5801\) |
Rank
sage: E.rank()
The elliptic curves in class 8624s have rank \(1\).
Complex multiplication
The elliptic curves in class 8624s do not have complex multiplication.Modular form 8624.2.a.s
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.