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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 222180.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
222180.s1 | 222180d2 | \([0, 1, 0, -2660, 52308]\) | \(-15375747664/128625\) | \(-17418912000\) | \([]\) | \(217728\) | \(0.79122\) | |
222180.s2 | 222180d1 | \([0, 1, 0, 100, 420]\) | \(808496/945\) | \(-127975680\) | \([]\) | \(72576\) | \(0.24191\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 222180.s have rank \(1\).
Complex multiplication
The elliptic curves in class 222180.s do not have complex multiplication.Modular form 222180.2.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.