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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 21840.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21840.bo1 | 21840q4 | \([0, 1, 0, -24976, 1510964]\) | \(841356017734178/1404585\) | \(2876590080\) | \([2]\) | \(40960\) | \(1.0772\) | |
| 21840.bo2 | 21840q3 | \([0, 1, 0, -4096, -71020]\) | \(3711757787138/1124589375\) | \(2303159040000\) | \([2]\) | \(40960\) | \(1.0772\) | |
| 21840.bo3 | 21840q2 | \([0, 1, 0, -1576, 22724]\) | \(423026849956/16769025\) | \(17171481600\) | \([2, 2]\) | \(20480\) | \(0.73060\) | |
| 21840.bo4 | 21840q1 | \([0, 1, 0, 44, 1340]\) | \(35969456/2985255\) | \(-764225280\) | \([2]\) | \(10240\) | \(0.38403\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 21840.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 21840.bo do not have complex multiplication.Modular form 21840.2.a.bo
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
