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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 88935.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88935.bv1 | 88935bq6 | \([1, 0, 1, -78559374, -268000082759]\) | \(257260669489908001/14267882475\) | \(2973746024269632040275\) | \([2]\) | \(11796480\) | \(3.1858\) | |
| 88935.bv2 | 88935bq4 | \([1, 0, 1, -5187999, -3687041459]\) | \(74093292126001/14707625625\) | \(3065398338220466180625\) | \([2, 2]\) | \(5898240\) | \(2.8392\) | |
| 88935.bv3 | 88935bq2 | \([1, 0, 1, -1600954, 727893527]\) | \(2177286259681/161417025\) | \(33642920537385615225\) | \([2, 2]\) | \(2949120\) | \(2.4926\) | |
| 88935.bv4 | 88935bq1 | \([1, 0, 1, -1571309, 757989131]\) | \(2058561081361/12705\) | \(2648006339030745\) | \([2]\) | \(1474560\) | \(2.1460\) | \(\Gamma_0(N)\)-optimal |
| 88935.bv5 | 88935bq3 | \([1, 0, 1, 1511771, 3216828437]\) | \(1833318007919/22507682505\) | \(-4691104757979645642945\) | \([2]\) | \(5898240\) | \(2.8392\) | |
| 88935.bv6 | 88935bq5 | \([1, 0, 1, 10790656, -21915491083]\) | \(666688497209279/1381398046875\) | \(-287914268779983488671875\) | \([2]\) | \(11796480\) | \(3.1858\) |
Rank
sage: E.rank()
The elliptic curves in class 88935.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 88935.bv do not have complex multiplication.Modular form 88935.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
