Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 25200m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25200.fw1 | 25200m1 | \([0, 0, 0, -150, -625]\) | \(55296/7\) | \(47250000\) | \([2]\) | \(8192\) | \(0.20180\) | \(\Gamma_0(N)\)-optimal |
25200.fw2 | 25200m2 | \([0, 0, 0, 225, -3250]\) | \(11664/49\) | \(-5292000000\) | \([2]\) | \(16384\) | \(0.54837\) |
Rank
sage: E.rank()
The elliptic curves in class 25200m have rank \(0\).
Complex multiplication
The elliptic curves in class 25200m do not have complex multiplication.Modular form 25200.2.a.m
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 Cremona 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 Cremona labels.