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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 198744bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 198744.bd3 | 198744bv1 | \([0, -1, 0, -60727, 5741800]\) | \(2725888/21\) | \(190804068685776\) | \([2]\) | \(884736\) | \(1.5692\) | \(\Gamma_0(N)\)-optimal |
| 198744.bd2 | 198744bv2 | \([0, -1, 0, -102132, -3036060]\) | \(810448/441\) | \(64110167078420736\) | \([2, 2]\) | \(1769472\) | \(1.9158\) | |
| 198744.bd4 | 198744bv3 | \([0, -1, 0, 394728, -24301668]\) | \(11696828/7203\) | \(-4188530915790154752\) | \([2]\) | \(3538944\) | \(2.2624\) | |
| 198744.bd1 | 198744bv4 | \([0, -1, 0, -1261472, -544215972]\) | \(381775972/567\) | \(329709430689020928\) | \([2]\) | \(3538944\) | \(2.2624\) |
Rank
sage: E.rank()
The elliptic curves in class 198744bv have rank \(1\).
Complex multiplication
The elliptic curves in class 198744bv do not have complex multiplication.Modular form 198744.2.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.
