Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 27200l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27200.m2 | 27200l1 | \([0, 1, 0, -12008, 507238]\) | \(-191501383744/2088025\) | \(-2088025000000\) | \([2]\) | \(36864\) | \(1.1795\) | \(\Gamma_0(N)\)-optimal |
| 27200.m1 | 27200l2 | \([0, 1, 0, -192633, 32477863]\) | \(12352022024896/1445\) | \(92480000000\) | \([2]\) | \(73728\) | \(1.5261\) |
Rank
sage: E.rank()
The elliptic curves in class 27200l have rank \(1\).
Complex multiplication
The elliptic curves in class 27200l do not have complex multiplication.Modular form 27200.2.a.l
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.
