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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 389376x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
389376.x2 | 389376x1 | \([0, 0, 0, 312, 10816]\) | \(64\) | \(-52481654784\) | \([]\) | \(230400\) | \(0.73758\) | \(\Gamma_0(N)\)-optimal |
389376.x1 | 389376x2 | \([0, 0, 0, -224328, 40895296]\) | \(-23788477376\) | \(-52481654784\) | \([]\) | \(1152000\) | \(1.5423\) |
Rank
sage: E.rank()
The elliptic curves in class 389376x have rank \(2\).
Complex multiplication
The elliptic curves in class 389376x do not have complex multiplication.Modular form 389376.2.a.x
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 Cremona 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 Cremona labels.