Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 296208i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296208.i1 | 296208i1 | \([0, 0, 0, -743787, -246887190]\) | \(34410094596/2057\) | \(2720306802926592\) | \([2]\) | \(4177920\) | \(2.0231\) | \(\Gamma_0(N)\)-optimal |
296208.i2 | 296208i2 | \([0, 0, 0, -700227, -277074270]\) | \(-14355776178/4231249\) | \(-11191342187239999488\) | \([2]\) | \(8355840\) | \(2.3696\) |
Rank
sage: E.rank()
The elliptic curves in class 296208i have rank \(1\).
Complex multiplication
The elliptic curves in class 296208i do not have complex multiplication.Modular form 296208.2.a.i
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 Cremona 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 Cremona labels.