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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 40560.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.g1 | 40560a6 | \([0, -1, 0, -540856, 153278800]\) | \(1770025017602/75\) | \(741397862400\) | \([2]\) | \(245760\) | \(1.7625\) | |
| 40560.g2 | 40560a4 | \([0, -1, 0, -33856, 2395600]\) | \(868327204/5625\) | \(27802419840000\) | \([2, 2]\) | \(122880\) | \(1.4159\) | |
| 40560.g3 | 40560a5 | \([0, -1, 0, -13576, 5218576]\) | \(-27995042/1171875\) | \(-11584341600000000\) | \([2]\) | \(245760\) | \(1.7625\) | |
| 40560.g4 | 40560a2 | \([0, -1, 0, -3436, -13664]\) | \(3631696/2025\) | \(2502217785600\) | \([2, 2]\) | \(61440\) | \(1.0693\) | |
| 40560.g5 | 40560a1 | \([0, -1, 0, -2591, -49830]\) | \(24918016/45\) | \(3475302480\) | \([2]\) | \(30720\) | \(0.72275\) | \(\Gamma_0(N)\)-optimal |
| 40560.g6 | 40560a3 | \([0, -1, 0, 13464, -121824]\) | \(54607676/32805\) | \(-162143712506880\) | \([2]\) | \(122880\) | \(1.4159\) |
Rank
sage: E.rank()
The elliptic curves in class 40560.g have rank \(1\).
Complex multiplication
The elliptic curves in class 40560.g do not have complex multiplication.Modular form 40560.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
