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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1862.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1862.b1 | 1862b3 | \([1, 1, 0, -4190, 838132]\) | \(-69173457625/2550136832\) | \(-300021048147968\) | \([]\) | \(6804\) | \(1.4581\) | |
| 1862.b2 | 1862b1 | \([1, 1, 0, -760, -8392]\) | \(-413493625/152\) | \(-17882648\) | \([]\) | \(756\) | \(0.35951\) | \(\Gamma_0(N)\)-optimal |
| 1862.b3 | 1862b2 | \([1, 1, 0, 465, -30491]\) | \(94196375/3511808\) | \(-413160699392\) | \([]\) | \(2268\) | \(0.90882\) |
Rank
sage: E.rank()
The elliptic curves in class 1862.b have rank \(0\).
Complex multiplication
The elliptic curves in class 1862.b do not have complex multiplication.Modular form 1862.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
