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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 270504bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270504.bv3 | 270504bv1 | \([0, 0, 0, -19074, -584647]\) | \(2725888/1053\) | \(296462256871248\) | \([2]\) | \(655360\) | \(1.4759\) | \(\Gamma_0(N)\)-optimal |
| 270504.bv2 | 270504bv2 | \([0, 0, 0, -136119, 18915050]\) | \(61918288/1521\) | \(6851572158802176\) | \([2, 2]\) | \(1310720\) | \(1.8225\) | |
| 270504.bv1 | 270504bv3 | \([0, 0, 0, -2164899, 1226039150]\) | \(62275269892/39\) | \(702725349620736\) | \([2]\) | \(2621440\) | \(2.1690\) | |
| 270504.bv4 | 270504bv4 | \([0, 0, 0, 19941, 59771558]\) | \(48668/85683\) | \(-1543887593116756992\) | \([2]\) | \(2621440\) | \(2.1690\) |
Rank
sage: E.rank()
The elliptic curves in class 270504bv have rank \(1\).
Complex multiplication
The elliptic curves in class 270504bv do not have complex multiplication.Modular form 270504.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
