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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 22050bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22050.d2 | 22050bv1 | \([1, -1, 0, 269883, -4455459]\) | \(2595575/1512\) | \(-1266390380390625000\) | \([]\) | \(414720\) | \(2.1630\) | \(\Gamma_0(N)\)-optimal |
| 22050.d1 | 22050bv2 | \([1, -1, 0, -3864492, -3092833584]\) | \(-7620530425/526848\) | \(-441266692545000000000\) | \([]\) | \(1244160\) | \(2.7123\) |
Rank
sage: E.rank()
The elliptic curves in class 22050bv have rank \(1\).
Complex multiplication
The elliptic curves in class 22050bv do not have complex multiplication.Modular form 22050.2.a.bv
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
