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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 34914.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34914.s1 | 34914r2 | \([1, 0, 1, -184745062, 966496857272]\) | \(4710588959856854135593/81253269504\) | \(12028399985181229056\) | \([]\) | \(4561920\) | \(3.2024\) | |
34914.s2 | 34914r1 | \([1, 0, 1, -2422567, 1151479178]\) | \(10621450496611513/2276047011744\) | \(336936642789316480416\) | \([]\) | \(1520640\) | \(2.6531\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34914.s have rank \(0\).
Complex multiplication
The elliptic curves in class 34914.s do not have complex multiplication.Modular form 34914.2.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.