Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4928.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4928.c1 | 4928w2 | \([0, 1, 0, -929, 10591]\) | \(1354435492/539\) | \(35323904\) | \([2]\) | \(2048\) | \(0.41229\) | |
4928.c2 | 4928w1 | \([0, 1, 0, -49, 207]\) | \(-810448/847\) | \(-13877248\) | \([2]\) | \(1024\) | \(0.065713\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4928.c have rank \(2\).
Complex multiplication
The elliptic curves in class 4928.c do not have complex multiplication.Modular form 4928.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.