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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 83490b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83490.a1 | 83490b1 | \([1, 1, 0, -92411068, 341881227472]\) | \(65571879529924849438074899/1736441856000000000\) | \(2311204110336000000000\) | \([2]\) | \(12386304\) | \(3.2047\) | \(\Gamma_0(N)\)-optimal |
83490.a2 | 83490b2 | \([1, 1, 0, -88806588, 369780623568]\) | \(-58194403089442524399708179/10712250000000000000000\) | \(-14258004750000000000000000\) | \([2]\) | \(24772608\) | \(3.5513\) |
Rank
sage: E.rank()
The elliptic curves in class 83490b have rank \(1\).
Complex multiplication
The elliptic curves in class 83490b do not have complex multiplication.Modular form 83490.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.