Show commands:
SageMath
E = EllipticCurve("fx1")
E.isogeny_class()
Elliptic curves in class 304704.fx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304704.fx1 | 304704fx2 | \([0, 0, 0, -32844, 2242960]\) | \(3370318/81\) | \(94168571314176\) | \([2]\) | \(1179648\) | \(1.4660\) | |
304704.fx2 | 304704fx1 | \([0, 0, 0, 276, 110032]\) | \(4/9\) | \(-5231587295232\) | \([2]\) | \(589824\) | \(1.1194\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 304704.fx have rank \(0\).
Complex multiplication
The elliptic curves in class 304704.fx do not have complex multiplication.Modular form 304704.2.a.fx
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.