Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1014.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1014.c1 | 1014b1 | \([1, 0, 1, -10482, 722308]\) | \(-156116857/186624\) | \(-152234930075904\) | \([3]\) | \(4992\) | \(1.4152\) | \(\Gamma_0(N)\)-optimal |
1014.c2 | 1014b2 | \([1, 0, 1, 88383, -13514252]\) | \(93603087383/150994944\) | \(-123171214536474624\) | \([]\) | \(14976\) | \(1.9645\) |
Rank
sage: E.rank()
The elliptic curves in class 1014.c have rank \(0\).
Complex multiplication
The elliptic curves in class 1014.c do not have complex multiplication.Modular form 1014.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.