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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 5929.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5929.b1 | 5929g2 | \([1, 0, 0, -305467, 59960550]\) | \(15124197817/1294139\) | \(269727530545998371\) | \([2]\) | \(69120\) | \(2.0859\) | |
5929.b2 | 5929g1 | \([1, 0, 0, 20628, 4328743]\) | \(4657463/41503\) | \(-8650154040833767\) | \([2]\) | \(34560\) | \(1.7393\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5929.b have rank \(1\).
Complex multiplication
The elliptic curves in class 5929.b do not have complex multiplication.Modular form 5929.2.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.