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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 37026bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37026.bo1 | 37026bc1 | \([1, -1, 1, -9824, -179517]\) | \(81182737/35904\) | \(46368865958976\) | \([2]\) | \(92160\) | \(1.3180\) | \(\Gamma_0(N)\)-optimal |
| 37026.bo2 | 37026bc2 | \([1, -1, 1, 33736, -1364349]\) | \(3288008303/2517768\) | \(-3251616725373192\) | \([2]\) | \(184320\) | \(1.6646\) |
Rank
sage: E.rank()
The elliptic curves in class 37026bc have rank \(0\).
Complex multiplication
The elliptic curves in class 37026bc do not have complex multiplication.Modular form 37026.2.a.bc
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.
