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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 12342.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12342.b1 | 12342f1 | \([1, 1, 0, -1091, 6285]\) | \(81182737/35904\) | \(63606126144\) | \([2]\) | \(11520\) | \(0.76871\) | \(\Gamma_0(N)\)-optimal |
12342.b2 | 12342f2 | \([1, 1, 0, 3749, 51781]\) | \(3288008303/2517768\) | \(-4460379595848\) | \([2]\) | \(23040\) | \(1.1153\) |
Rank
sage: E.rank()
The elliptic curves in class 12342.b have rank \(1\).
Complex multiplication
The elliptic curves in class 12342.b do not have complex multiplication.Modular form 12342.2.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.