Show commands:
SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 11970.cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11970.cj1 | 11970bm2 | \([1, -1, 1, -152, 749]\) | \(14295828483/176890\) | \(4776030\) | \([2]\) | \(3328\) | \(0.091581\) | |
11970.cj2 | 11970bm1 | \([1, -1, 1, -2, 29]\) | \(-19683/13300\) | \(-359100\) | \([2]\) | \(1664\) | \(-0.25499\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11970.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 11970.cj do not have complex multiplication.Modular form 11970.2.a.cj
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.