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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 6336.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6336.c1 | 6336bg3 | \([0, 0, 0, -5797452, 5372839280]\) | \(112763292123580561/1932612\) | \(369327904653312\) | \([2]\) | \(153600\) | \(2.3369\) | |
| 6336.c2 | 6336bg4 | \([0, 0, 0, -5791692, 5384048240]\) | \(-112427521449300721/466873642818\) | \(-89220942558480826368\) | \([2]\) | \(307200\) | \(2.6835\) | |
| 6336.c3 | 6336bg1 | \([0, 0, 0, -25932, -1171600]\) | \(10091699281/2737152\) | \(523077892964352\) | \([2]\) | \(30720\) | \(1.5322\) | \(\Gamma_0(N)\)-optimal |
| 6336.c4 | 6336bg2 | \([0, 0, 0, 66228, -7622800]\) | \(168105213359/228637728\) | \(-43693350246678528\) | \([2]\) | \(61440\) | \(1.8787\) |
Rank
sage: E.rank()
The elliptic curves in class 6336.c have rank \(1\).
Complex multiplication
The elliptic curves in class 6336.c do not have complex multiplication.Modular form 6336.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
