Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 392784r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 392784.r2 | 392784r1 | \([0, -1, 0, -1388, -215424]\) | \(-9826000/662823\) | \(-19962998560512\) | \([2]\) | \(737280\) | \(1.2318\) | \(\Gamma_0(N)\)-optimal |
| 392784.r1 | 392784r2 | \([0, -1, 0, -63128, -6043680]\) | \(230944958500/1757007\) | \(211671159340032\) | \([2]\) | \(1474560\) | \(1.5784\) |
Rank
sage: E.rank()
The elliptic curves in class 392784r have rank \(0\).
Complex multiplication
The elliptic curves in class 392784r do not have complex multiplication.Modular form 392784.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
