Show commands:
SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 44880.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44880.cc1 | 44880cc2 | \([0, 1, 0, -2296, -27820]\) | \(326940373369/112003650\) | \(458766950400\) | \([2]\) | \(49152\) | \(0.93960\) | |
44880.cc2 | 44880cc1 | \([0, 1, 0, 424, -2796]\) | \(2053225511/2098140\) | \(-8593981440\) | \([2]\) | \(24576\) | \(0.59303\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44880.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 44880.cc do not have complex multiplication.Modular form 44880.2.a.cc
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.