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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 142956.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142956.s1 | 142956n2 | \([0, 0, 0, -183540, -30272947]\) | \(-162390710272000/47832147\) | \(-201407012701488\) | \([]\) | \(466560\) | \(1.7236\) | |
142956.s2 | 142956n1 | \([0, 0, 0, 1140, -151639]\) | \(38912000/2381643\) | \(-10028393706672\) | \([]\) | \(155520\) | \(1.1743\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 142956.s have rank \(1\).
Complex multiplication
The elliptic curves in class 142956.s do not have complex multiplication.Modular form 142956.2.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.