Show commands:
SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 70560eh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70560.eg2 | 70560eh1 | \([0, 0, 0, -777, -196]\) | \(3241792/1875\) | \(30005640000\) | \([2]\) | \(65536\) | \(0.69987\) | \(\Gamma_0(N)\)-optimal |
70560.eg1 | 70560eh2 | \([0, 0, 0, -8652, -308896]\) | \(69934528/225\) | \(230443315200\) | \([2]\) | \(131072\) | \(1.0464\) |
Rank
sage: E.rank()
The elliptic curves in class 70560eh have rank \(1\).
Complex multiplication
The elliptic curves in class 70560eh do not have complex multiplication.Modular form 70560.2.a.eh
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.