Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 148720j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148720.v1 | 148720j1 | \([0, -1, 0, -239360, -45424640]\) | \(-76711450249/851840\) | \(-16841396136181760\) | \([]\) | \(1548288\) | \(1.9284\) | \(\Gamma_0(N)\)-optimal |
148720.v2 | 148720j2 | \([0, -1, 0, 801680, -236143168]\) | \(2882081488391/2883584000\) | \(-57010213697355776000\) | \([]\) | \(4644864\) | \(2.4777\) |
Rank
sage: E.rank()
The elliptic curves in class 148720j have rank \(0\).
Complex multiplication
The elliptic curves in class 148720j do not have complex multiplication.Modular form 148720.2.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 Cremona 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 Cremona labels.