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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 26950.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26950.x1 | 26950bh1 | \([1, -1, 0, -477367, 127036041]\) | \(52355598021/15092\) | \(3467888101562500\) | \([2]\) | \(276480\) | \(1.9619\) | \(\Gamma_0(N)\)-optimal |
26950.x2 | 26950bh2 | \([1, -1, 0, -416117, 160784791]\) | \(-34677868581/28471058\) | \(-6542170903597656250\) | \([2]\) | \(552960\) | \(2.3084\) |
Rank
sage: E.rank()
The elliptic curves in class 26950.x have rank \(1\).
Complex multiplication
The elliptic curves in class 26950.x do not have complex multiplication.Modular form 26950.2.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 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.