Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 6760.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6760.k1 | 6760c1 | \([0, -1, 0, -3436, -75180]\) | \(3631696/65\) | \(80318101760\) | \([2]\) | \(5376\) | \(0.88814\) | \(\Gamma_0(N)\)-optimal |
| 6760.k2 | 6760c2 | \([0, -1, 0, -56, -219844]\) | \(-4/4225\) | \(-20882706457600\) | \([2]\) | \(10752\) | \(1.2347\) |
Rank
sage: E.rank()
The elliptic curves in class 6760.k have rank \(1\).
Complex multiplication
The elliptic curves in class 6760.k do not have complex multiplication.Modular form 6760.2.a.k
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.
