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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 2880.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2880.y1 | 2880r7 | \([0, 0, 0, -1244172, 534156784]\) | \(1114544804970241/405\) | \(77396705280\) | \([2]\) | \(16384\) | \(1.8799\) | |
2880.y2 | 2880r5 | \([0, 0, 0, -77772, 8343664]\) | \(272223782641/164025\) | \(31345665638400\) | \([2, 2]\) | \(8192\) | \(1.5333\) | |
2880.y3 | 2880r8 | \([0, 0, 0, -63372, 11528944]\) | \(-147281603041/215233605\) | \(-41131782450708480\) | \([2]\) | \(16384\) | \(1.8799\) | |
2880.y4 | 2880r3 | \([0, 0, 0, -46092, -3808784]\) | \(56667352321/15\) | \(2866544640\) | \([2]\) | \(4096\) | \(1.1867\) | |
2880.y5 | 2880r4 | \([0, 0, 0, -5772, 78064]\) | \(111284641/50625\) | \(9674588160000\) | \([2, 2]\) | \(4096\) | \(1.1867\) | |
2880.y6 | 2880r2 | \([0, 0, 0, -2892, -59024]\) | \(13997521/225\) | \(42998169600\) | \([2, 2]\) | \(2048\) | \(0.84018\) | |
2880.y7 | 2880r1 | \([0, 0, 0, -12, -2576]\) | \(-1/15\) | \(-2866544640\) | \([2]\) | \(1024\) | \(0.49360\) | \(\Gamma_0(N)\)-optimal |
2880.y8 | 2880r6 | \([0, 0, 0, 20148, 586096]\) | \(4733169839/3515625\) | \(-671846400000000\) | \([2]\) | \(8192\) | \(1.5333\) |
Rank
sage: E.rank()
The elliptic curves in class 2880.y have rank \(1\).
Complex multiplication
The elliptic curves in class 2880.y do not have complex multiplication.Modular form 2880.2.a.y
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.