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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 229320.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.bv1 | 229320br4 | \([0, 0, 0, -618723, -187238898]\) | \(298261205316/156065\) | \(13706331826037760\) | \([2]\) | \(2359296\) | \(2.0469\) | |
| 229320.bv2 | 229320br3 | \([0, 0, 0, -354123, 79848342]\) | \(55920415716/999635\) | \(87792451958615040\) | \([2]\) | \(2359296\) | \(2.0469\) | |
| 229320.bv3 | 229320br2 | \([0, 0, 0, -45423, -1833678]\) | \(472058064/207025\) | \(4545467187206400\) | \([2, 2]\) | \(1179648\) | \(1.7003\) | |
| 229320.bv4 | 229320br1 | \([0, 0, 0, 9702, -213003]\) | \(73598976/56875\) | \(-78047170110000\) | \([2]\) | \(589824\) | \(1.3537\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 229320.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 229320.bv do not have complex multiplication.Modular form 229320.2.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 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.
