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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 14700s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14700.g1 | 14700s1 | \([0, -1, 0, -32258, -2367063]\) | \(-3155449600/250047\) | \(-294177795030000\) | \([]\) | \(62208\) | \(1.5232\) | \(\Gamma_0(N)\)-optimal |
14700.g2 | 14700s2 | \([0, -1, 0, 188242, -999963]\) | \(627021958400/363182463\) | \(-427280535894870000\) | \([]\) | \(186624\) | \(2.0725\) |
Rank
sage: E.rank()
The elliptic curves in class 14700s have rank \(0\).
Complex multiplication
The elliptic curves in class 14700s do not have complex multiplication.Modular form 14700.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.