Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 180708.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
180708.g1 | 180708i2 | \([0, -1, 0, -214697988, 1210920788808]\) | \(1666315860501346000/40252707\) | \(26439022946211625728\) | \([2]\) | \(15759360\) | \(3.2468\) | |
180708.g2 | 180708i1 | \([0, -1, 0, -13434453, 18877123710]\) | \(6532108386304000/31987847133\) | \(1313153026499088566352\) | \([2]\) | \(7879680\) | \(2.9002\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 180708.g have rank \(1\).
Complex multiplication
The elliptic curves in class 180708.g do not have complex multiplication.Modular form 180708.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.