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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 2760.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2760.e1 | 2760f5 | \([0, -1, 0, -870880, -301514900]\) | \(35667215800077781442/1427217706746225\) | \(2922941863416268800\) | \([2]\) | \(43008\) | \(2.3097\) | |
| 2760.e2 | 2760f3 | \([0, -1, 0, -141880, 14287900]\) | \(308453964046598884/92949363050625\) | \(95180147763840000\) | \([2, 2]\) | \(21504\) | \(1.9631\) | |
| 2760.e3 | 2760f2 | \([0, -1, 0, -129380, 17952900]\) | \(935596404100595536/150641015625\) | \(38564100000000\) | \([2, 4]\) | \(10752\) | \(1.6165\) | |
| 2760.e4 | 2760f1 | \([0, -1, 0, -129375, 17954352]\) | \(14967807005098080256/388125\) | \(6210000\) | \([4]\) | \(5376\) | \(1.2699\) | \(\Gamma_0(N)\)-optimal |
| 2760.e5 | 2760f4 | \([0, -1, 0, -116960, 21524892]\) | \(-172798332611391364/94757080078125\) | \(-97031250000000000\) | \([4]\) | \(21504\) | \(1.9631\) | |
| 2760.e6 | 2760f6 | \([0, -1, 0, 387120, 95330700]\) | \(3132776881711582558/3735130619961225\) | \(-7649547509680588800\) | \([2]\) | \(43008\) | \(2.3097\) |
Rank
sage: E.rank()
The elliptic curves in class 2760.e have rank \(1\).
Complex multiplication
The elliptic curves in class 2760.e do not have complex multiplication.Modular form 2760.2.a.e
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.
