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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 8280.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8280.g1 | 8280i5 | \([0, 0, 0, -7837923, 8148740222]\) | \(35667215800077781442/1427217706746225\) | \(2130824618430459955200\) | \([2]\) | \(344064\) | \(2.8590\) | |
| 8280.g2 | 8280i3 | \([0, 0, 0, -1276923, -384496378]\) | \(308453964046598884/92949363050625\) | \(69386327719839360000\) | \([2, 2]\) | \(172032\) | \(2.5124\) | |
| 8280.g3 | 8280i2 | \([0, 0, 0, -1164423, -483563878]\) | \(935596404100595536/150641015625\) | \(28113228900000000\) | \([2, 2]\) | \(86016\) | \(2.1658\) | |
| 8280.g4 | 8280i1 | \([0, 0, 0, -1164378, -483603127]\) | \(14967807005098080256/388125\) | \(4527090000\) | \([2]\) | \(43008\) | \(1.8192\) | \(\Gamma_0(N)\)-optimal |
| 8280.g5 | 8280i4 | \([0, 0, 0, -1052643, -580119442]\) | \(-172798332611391364/94757080078125\) | \(-70735781250000000000\) | \([2]\) | \(172032\) | \(2.5124\) | |
| 8280.g6 | 8280i6 | \([0, 0, 0, 3484077, -2577412978]\) | \(3132776881711582558/3735130619961225\) | \(-5576520134557149235200\) | \([2]\) | \(344064\) | \(2.8590\) |
Rank
sage: E.rank()
The elliptic curves in class 8280.g have rank \(1\).
Complex multiplication
The elliptic curves in class 8280.g do not have complex multiplication.Modular form 8280.2.a.g
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.
