Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 179860.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179860.g1 | 179860e1 | \([0, 0, 0, -14812, -693519]\) | \(151732224/85\) | \(201328809040\) | \([2]\) | \(304128\) | \(1.1162\) | \(\Gamma_0(N)\)-optimal |
179860.g2 | 179860e2 | \([0, 0, 0, -12167, -949026]\) | \(-5256144/7225\) | \(-273807180294400\) | \([2]\) | \(608256\) | \(1.4628\) |
Rank
sage: E.rank()
The elliptic curves in class 179860.g have rank \(0\).
Complex multiplication
The elliptic curves in class 179860.g do not have complex multiplication.Modular form 179860.2.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.