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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 7406.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7406.b1 | 7406a2 | \([1, -1, 0, -247142, 46926408]\) | \(926859375/9604\) | \(17298270160690652\) | \([2]\) | \(52992\) | \(1.9328\) | |
7406.b2 | 7406a1 | \([1, -1, 0, -3802, 1811172]\) | \(-3375/784\) | \(-1412103686586992\) | \([2]\) | \(26496\) | \(1.5862\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7406.b have rank \(0\).
Complex multiplication
The elliptic curves in class 7406.b do not have complex multiplication.Modular form 7406.2.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.