Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 185150.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185150.i1 | 185150bt2 | \([1, 1, 0, -24080, 2010970]\) | \(-417267265/235298\) | \(-870813715248050\) | \([]\) | \(912384\) | \(1.5699\) | |
185150.i2 | 185150bt1 | \([1, 1, 0, 2370, -36260]\) | \(397535/392\) | \(-1450751712200\) | \([]\) | \(304128\) | \(1.0206\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185150.i have rank \(1\).
Complex multiplication
The elliptic curves in class 185150.i do not have complex multiplication.Modular form 185150.2.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.