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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 42483.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42483.s1 | 42483q2 | \([0, 1, 1, -840219, 296323514]\) | \(-23100424192/14739\) | \(-41855235245986659\) | \([]\) | \(497664\) | \(2.1303\) | |
42483.s2 | 42483q1 | \([0, 1, 1, 9441, 1703909]\) | \(32768/459\) | \(-1303450232573979\) | \([]\) | \(165888\) | \(1.5810\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 42483.s have rank \(1\).
Complex multiplication
The elliptic curves in class 42483.s do not have complex multiplication.Modular form 42483.2.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 LMFDB 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 LMFDB labels.