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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 17424.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17424.s1 | 17424bu2 | \([0, 0, 0, -43923, 13850386]\) | \(-121\) | \(-77448734859792384\) | \([]\) | \(101376\) | \(1.9234\) | |
17424.s2 | 17424bu1 | \([0, 0, 0, -4323, -109406]\) | \(-24729001\) | \(-361304064\) | \([]\) | \(9216\) | \(0.72449\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17424.s have rank \(0\).
Complex multiplication
The elliptic curves in class 17424.s do not have complex multiplication.Modular form 17424.2.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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.