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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 2880bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2880.bc7 | 2880bd1 | \([0, 0, 0, -12, 2576]\) | \(-1/15\) | \(-2866544640\) | \([2]\) | \(1024\) | \(0.49360\) | \(\Gamma_0(N)\)-optimal |
| 2880.bc6 | 2880bd2 | \([0, 0, 0, -2892, 59024]\) | \(13997521/225\) | \(42998169600\) | \([2, 2]\) | \(2048\) | \(0.84018\) | |
| 2880.bc5 | 2880bd3 | \([0, 0, 0, -5772, -78064]\) | \(111284641/50625\) | \(9674588160000\) | \([2, 2]\) | \(4096\) | \(1.1867\) | |
| 2880.bc4 | 2880bd4 | \([0, 0, 0, -46092, 3808784]\) | \(56667352321/15\) | \(2866544640\) | \([2]\) | \(4096\) | \(1.1867\) | |
| 2880.bc2 | 2880bd5 | \([0, 0, 0, -77772, -8343664]\) | \(272223782641/164025\) | \(31345665638400\) | \([2, 2]\) | \(8192\) | \(1.5333\) | |
| 2880.bc8 | 2880bd6 | \([0, 0, 0, 20148, -586096]\) | \(4733169839/3515625\) | \(-671846400000000\) | \([2]\) | \(8192\) | \(1.5333\) | |
| 2880.bc1 | 2880bd7 | \([0, 0, 0, -1244172, -534156784]\) | \(1114544804970241/405\) | \(77396705280\) | \([2]\) | \(16384\) | \(1.8799\) | |
| 2880.bc3 | 2880bd8 | \([0, 0, 0, -63372, -11528944]\) | \(-147281603041/215233605\) | \(-41131782450708480\) | \([2]\) | \(16384\) | \(1.8799\) |
Rank
sage: E.rank()
The elliptic curves in class 2880bd have rank \(0\).
Complex multiplication
The elliptic curves in class 2880bd do not have complex multiplication.Modular form 2880.2.a.bd
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
