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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 68544.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68544.b1 | 68544cs2 | \([0, 0, 0, -403212, -98348560]\) | \(37936442980801/88817792\) | \(16973344372948992\) | \([2]\) | \(1032192\) | \(1.9945\) | |
68544.b2 | 68544cs1 | \([0, 0, 0, -34572, -290320]\) | \(23912763841/13647872\) | \(2608148955267072\) | \([2]\) | \(516096\) | \(1.6479\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 68544.b have rank \(0\).
Complex multiplication
The elliptic curves in class 68544.b do not have complex multiplication.Modular form 68544.2.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.