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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 35322.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35322.s1 | 35322q2 | \([1, 0, 1, -6140159, 5855610854]\) | \(43040219271568849/841158108\) | \(500340459286636668\) | \([2]\) | \(1451520\) | \(2.5182\) | |
35322.s2 | 35322q1 | \([1, 0, 1, -370899, 97889374]\) | \(-9486391169809/1473906672\) | \(-876714061483097712\) | \([2]\) | \(725760\) | \(2.1717\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35322.s have rank \(0\).
Complex multiplication
The elliptic curves in class 35322.s do not have complex multiplication.Modular form 35322.2.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.