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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 6370bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6370.l1 | 6370bb1 | \([1, 0, 0, -41210, 3216100]\) | \(65787589563409/10400000\) | \(1223549600000\) | \([2]\) | \(23040\) | \(1.3299\) | \(\Gamma_0(N)\)-optimal |
| 6370.l2 | 6370bb2 | \([1, 0, 0, -37290, 3853492]\) | \(-48743122863889/26406250000\) | \(-3106668906250000\) | \([2]\) | \(46080\) | \(1.6765\) |
Rank
sage: E.rank()
The elliptic curves in class 6370bb have rank \(1\).
Complex multiplication
The elliptic curves in class 6370bb do not have complex multiplication.Modular form 6370.2.a.bb
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.
