Show commands:
SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 12240.ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12240.ch1 | 12240cb1 | \([0, 0, 0, -252, 1539]\) | \(151732224/85\) | \(991440\) | \([2]\) | \(3072\) | \(0.097760\) | \(\Gamma_0(N)\)-optimal |
12240.ch2 | 12240cb2 | \([0, 0, 0, -207, 2106]\) | \(-5256144/7225\) | \(-1348358400\) | \([2]\) | \(6144\) | \(0.44433\) |
Rank
sage: E.rank()
The elliptic curves in class 12240.ch have rank \(0\).
Complex multiplication
The elliptic curves in class 12240.ch do not have complex multiplication.Modular form 12240.2.a.ch
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.