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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 53724b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53724.b2 | 53724b1 | \([0, -1, 0, -1187413, -495517394]\) | \(6532108386304000/31987847133\) | \(906694759276553808\) | \([2]\) | \(691200\) | \(2.2937\) | \(\Gamma_0(N)\)-optimal |
| 53724.b1 | 53724b2 | \([0, -1, 0, -18976228, -31810947320]\) | \(1666315860501346000/40252707\) | \(18255392221600512\) | \([2]\) | \(1382400\) | \(2.6403\) |
Rank
sage: E.rank()
The elliptic curves in class 53724b have rank \(1\).
Complex multiplication
The elliptic curves in class 53724b do not have complex multiplication.Modular form 53724.2.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 Cremona 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 Cremona labels.
