Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2304.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2304.j1 | 2304l2 | \([0, 0, 0, -840, 9344]\) | \(2744000/9\) | \(214990848\) | \([2]\) | \(1024\) | \(0.46417\) | |
2304.j2 | 2304l1 | \([0, 0, 0, -30, 272]\) | \(-8000/81\) | \(-30233088\) | \([2]\) | \(512\) | \(0.11759\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2304.j have rank \(1\).
Complex multiplication
The elliptic curves in class 2304.j do not have complex multiplication.Modular form 2304.2.a.j
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.