Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1248.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1248.g1 | 1248i1 | \([0, 1, 0, -14, 12]\) | \(5088448/1053\) | \(67392\) | \([2]\) | \(128\) | \(-0.35830\) | \(\Gamma_0(N)\)-optimal |
1248.g2 | 1248i2 | \([0, 1, 0, 31, 111]\) | \(778688/1521\) | \(-6230016\) | \([2]\) | \(256\) | \(-0.011725\) |
Rank
sage: E.rank()
The elliptic curves in class 1248.g have rank \(1\).
Complex multiplication
The elliptic curves in class 1248.g do not have complex multiplication.Modular form 1248.2.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.