Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 201810.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
201810.i1 | 201810cs1 | \([1, 1, 0, -2298, -174348]\) | \(-1397480182249/12706092000\) | \(-12210554412000\) | \([]\) | \(518400\) | \(1.1936\) | \(\Gamma_0(N)\)-optimal |
201810.i2 | 201810cs2 | \([1, 1, 0, 20487, 4441893]\) | \(989469253569191/9408000000000\) | \(-9041088000000000\) | \([]\) | \(1555200\) | \(1.7429\) |
Rank
sage: E.rank()
The elliptic curves in class 201810.i have rank \(1\).
Complex multiplication
The elliptic curves in class 201810.i do not have complex multiplication.Modular form 201810.2.a.i
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.