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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 40560.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.bv1 | 40560ca8 | \([0, 1, 0, -5840696, 5431120020]\) | \(1114544804970241/405\) | \(8007096913920\) | \([2]\) | \(589824\) | \(2.2665\) | |
| 40560.bv2 | 40560ca6 | \([0, 1, 0, -365096, 84744180]\) | \(272223782641/164025\) | \(3242874250137600\) | \([2, 2]\) | \(294912\) | \(1.9199\) | |
| 40560.bv3 | 40560ca7 | \([0, 1, 0, -297496, 117165140]\) | \(-147281603041/215233605\) | \(-4255299591030558720\) | \([2]\) | \(589824\) | \(2.2665\) | |
| 40560.bv4 | 40560ca4 | \([0, 1, 0, -216376, -38812396]\) | \(56667352321/15\) | \(296559144960\) | \([2]\) | \(147456\) | \(1.5733\) | |
| 40560.bv5 | 40560ca3 | \([0, 1, 0, -27096, 784980]\) | \(111284641/50625\) | \(1000887114240000\) | \([2, 2]\) | \(147456\) | \(1.5733\) | |
| 40560.bv6 | 40560ca2 | \([0, 1, 0, -13576, -604876]\) | \(13997521/225\) | \(4448387174400\) | \([2, 2]\) | \(73728\) | \(1.2268\) | |
| 40560.bv7 | 40560ca1 | \([0, 1, 0, -56, -26220]\) | \(-1/15\) | \(-296559144960\) | \([2]\) | \(36864\) | \(0.88020\) | \(\Gamma_0(N)\)-optimal |
| 40560.bv8 | 40560ca5 | \([0, 1, 0, 94584, 5992884]\) | \(4733169839/3515625\) | \(-69506049600000000\) | \([2]\) | \(294912\) | \(1.9199\) |
Rank
sage: E.rank()
The elliptic curves in class 40560.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 40560.bv do not have complex multiplication.Modular form 40560.2.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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
