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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 242760.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
242760.b1 | 242760b2 | \([0, -1, 0, -133036, -18618140]\) | \(42140629456/37485\) | \(231627974135040\) | \([2]\) | \(1474560\) | \(1.6813\) | |
242760.b2 | 242760b1 | \([0, -1, 0, -10211, -145260]\) | \(304900096/151725\) | \(58596362504400\) | \([2]\) | \(737280\) | \(1.3347\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242760.b have rank \(0\).
Complex multiplication
The elliptic curves in class 242760.b do not have complex multiplication.Modular form 242760.2.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 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.