Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 18928.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18928.j1 | 18928y2 | \([0, -1, 0, -992, 12544]\) | \(-156116857/2744\) | \(-1899462656\) | \([]\) | \(10368\) | \(0.57771\) | |
18928.j2 | 18928y1 | \([0, -1, 0, 48, 64]\) | \(17303/14\) | \(-9691136\) | \([]\) | \(3456\) | \(0.028402\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18928.j have rank \(1\).
Complex multiplication
The elliptic curves in class 18928.j do not have complex multiplication.Modular form 18928.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.