Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 81120.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81120.g1 | 81120z4 | \([0, -1, 0, -27096, -1707720]\) | \(890277128/15\) | \(37069893120\) | \([2]\) | \(147456\) | \(1.1583\) | |
81120.g2 | 81120z3 | \([0, -1, 0, -6816, 192516]\) | \(14172488/1875\) | \(4633736640000\) | \([2]\) | \(147456\) | \(1.1583\) | |
81120.g3 | 81120z1 | \([0, -1, 0, -1746, -24480]\) | \(1906624/225\) | \(69506049600\) | \([2, 2]\) | \(73728\) | \(0.81170\) | \(\Gamma_0(N)\)-optimal |
81120.g4 | 81120z2 | \([0, -1, 0, 2479, -128415]\) | \(85184/405\) | \(-8007096913920\) | \([2]\) | \(147456\) | \(1.1583\) |
Rank
sage: E.rank()
The elliptic curves in class 81120.g have rank \(0\).
Complex multiplication
The elliptic curves in class 81120.g do not have complex multiplication.Modular form 81120.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.