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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 187200.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.s1 | 187200e2 | \([0, 0, 0, -5240460, -4254722800]\) | \(666276475992821/58199166792\) | \(1390254246833946624000\) | \([2]\) | \(9437184\) | \(2.7975\) | |
187200.s2 | 187200e1 | \([0, 0, 0, -5125260, -4465999600]\) | \(623295446073461/5458752\) | \(130397969055744000\) | \([2]\) | \(4718592\) | \(2.4510\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 187200.s have rank \(0\).
Complex multiplication
The elliptic curves in class 187200.s do not have complex multiplication.Modular form 187200.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.