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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 96330.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96330.bl1 | 96330bn4 | \([1, 0, 1, -78286043, 170235850358]\) | \(10993009831928446009969/3767761230468750000\) | \(18186263817077636718750000\) | \([2]\) | \(37324800\) | \(3.5488\) | |
| 96330.bl2 | 96330bn2 | \([1, 0, 1, -70133483, 226060638806]\) | \(7903870428425797297009/886464000000\) | \(4278792413376000000\) | \([2]\) | \(12441600\) | \(2.9995\) | |
| 96330.bl3 | 96330bn1 | \([1, 0, 1, -4372203, 3550771798]\) | \(-1914980734749238129/20440940544000\) | \(-98664515786244096000\) | \([2]\) | \(6220800\) | \(2.6530\) | \(\Gamma_0(N)\)-optimal |
| 96330.bl4 | 96330bn3 | \([1, 0, 1, 14447637, 18486456406]\) | \(69096190760262356111/70568821500000000\) | \(-340622222735593500000000\) | \([2]\) | \(18662400\) | \(3.2023\) |
Rank
sage: E.rank()
The elliptic curves in class 96330.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 96330.bl do not have complex multiplication.Modular form 96330.2.a.bl
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
