Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 138600p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 138600.m2 | 138600p1 | \([0, 0, 0, -6995190, 7996969325]\) | \(-25963589461091772416/3923372657421063\) | \(-5720277334519909854000\) | \([2]\) | \(6451200\) | \(2.9043\) | \(\Gamma_0(N)\)-optimal |
| 138600.m1 | 138600p2 | \([0, 0, 0, -115704615, 479034907850]\) | \(7343418009347613339536/136478763980097\) | \(3183776606127702816000\) | \([2]\) | \(12902400\) | \(3.2509\) |
Rank
sage: E.rank()
The elliptic curves in class 138600p have rank \(0\).
Complex multiplication
The elliptic curves in class 138600p do not have complex multiplication.Modular form 138600.2.a.p
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.
