Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 10304.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10304.j1 | 10304bb2 | \([0, 1, 0, -257, -833]\) | \(57512456/25921\) | \(849379328\) | \([2]\) | \(4608\) | \(0.40859\) | |
10304.j2 | 10304bb1 | \([0, 1, 0, -217, -1305]\) | \(277167808/161\) | \(659456\) | \([2]\) | \(2304\) | \(0.062021\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10304.j have rank \(1\).
Complex multiplication
The elliptic curves in class 10304.j do not have complex multiplication.Modular form 10304.2.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.