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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 83790b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83790.p2 | 83790b1 | \([1, -1, 0, -10005, -1427455]\) | \(-47832147/353780\) | \(-819243133759260\) | \([2]\) | \(331776\) | \(1.5447\) | \(\Gamma_0(N)\)-optimal |
| 83790.p1 | 83790b2 | \([1, -1, 0, -261375, -51248989]\) | \(852780481587/2280950\) | \(5281962309763650\) | \([2]\) | \(663552\) | \(1.8912\) |
Rank
sage: E.rank()
The elliptic curves in class 83790b have rank \(0\).
Complex multiplication
The elliptic curves in class 83790b do not have complex multiplication.Modular form 83790.2.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.
