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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 389376.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
389376.s1 | 389376s2 | \([0, 0, 0, -224328, -40895296]\) | \(-23788477376\) | \(-52481654784\) | \([]\) | \(1152000\) | \(1.5423\) | |
389376.s2 | 389376s1 | \([0, 0, 0, 312, -10816]\) | \(64\) | \(-52481654784\) | \([]\) | \(230400\) | \(0.73758\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 389376.s have rank \(1\).
Complex multiplication
The elliptic curves in class 389376.s do not have complex multiplication.Modular form 389376.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.