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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 74704.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
74704.s1 | 74704q2 | \([0, -1, 0, -5888, 5888]\) | \(5512402554625/3188422748\) | \(13059779575808\) | \([2]\) | \(129024\) | \(1.2062\) | |
74704.s2 | 74704q1 | \([0, -1, 0, 1472, 0]\) | \(86058173375/49827568\) | \(-204093718528\) | \([2]\) | \(64512\) | \(0.85962\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 74704.s have rank \(1\).
Complex multiplication
The elliptic curves in class 74704.s do not have complex multiplication.Modular form 74704.2.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.