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SageMath
E = EllipticCurve("gc1")
E.isogeny_class()
Elliptic curves in class 116160.gc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116160.gc1 | 116160cs4 | \([0, 1, 0, -77601, 8294559]\) | \(890277128/15\) | \(870757662720\) | \([2]\) | \(368640\) | \(1.4213\) | |
| 116160.gc2 | 116160cs3 | \([0, 1, 0, -19521, -928545]\) | \(14172488/1875\) | \(108844707840000\) | \([2]\) | \(368640\) | \(1.4213\) | |
| 116160.gc3 | 116160cs2 | \([0, 1, 0, -5001, 119799]\) | \(1906624/225\) | \(1632670617600\) | \([2, 2]\) | \(184320\) | \(1.0748\) | |
| 116160.gc4 | 116160cs1 | \([0, 1, 0, 444, 9810]\) | \(85184/405\) | \(-45918861120\) | \([2]\) | \(92160\) | \(0.72818\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116160.gc have rank \(1\).
Complex multiplication
The elliptic curves in class 116160.gc do not have complex multiplication.Modular form 116160.2.a.gc
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
