Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 3150.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3150.x1 | 3150bh2 | \([1, -1, 1, -410, 4587]\) | \(-417267265/235298\) | \(-4288306050\) | \([]\) | \(2160\) | \(0.55144\) | |
3150.x2 | 3150bh1 | \([1, -1, 1, 40, -93]\) | \(397535/392\) | \(-7144200\) | \([]\) | \(720\) | \(0.0021345\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3150.x have rank \(1\).
Complex multiplication
The elliptic curves in class 3150.x do not have complex multiplication.Modular form 3150.2.a.x
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.