Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 19074.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19074.i1 | 19074k2 | \([1, 0, 1, -862527, -307608590]\) | \(2940001530995593/8673562656\) | \(209358717085023264\) | \([2]\) | \(276480\) | \(2.1936\) | |
19074.i2 | 19074k1 | \([1, 0, 1, -76447, -408526]\) | \(2046931732873/1181672448\) | \(28522700248998912\) | \([2]\) | \(138240\) | \(1.8470\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19074.i have rank \(1\).
Complex multiplication
The elliptic curves in class 19074.i do not have complex multiplication.Modular form 19074.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.