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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 2352b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2352.h2 | 2352b1 | \([0, -1, 0, 572, 13504]\) | \(2000/9\) | \(-92974710528\) | \([2]\) | \(1792\) | \(0.78707\) | \(\Gamma_0(N)\)-optimal |
| 2352.h1 | 2352b2 | \([0, -1, 0, -6288, 172656]\) | \(665500/81\) | \(3347089579008\) | \([2]\) | \(3584\) | \(1.1336\) |
Rank
sage: E.rank()
The elliptic curves in class 2352b have rank \(0\).
Complex multiplication
The elliptic curves in class 2352b do not have complex multiplication.Modular form 2352.2.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.
