Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 3036.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3036.d1 | 3036d2 | \([0, -1, 0, -228, 936]\) | \(5142706000/1728243\) | \(442430208\) | \([2]\) | \(1152\) | \(0.36142\) | |
3036.d2 | 3036d1 | \([0, -1, 0, -93, -306]\) | \(5619712000/184437\) | \(2950992\) | \([2]\) | \(576\) | \(0.014845\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3036.d have rank \(1\).
Complex multiplication
The elliptic curves in class 3036.d do not have complex multiplication.Modular form 3036.2.a.d
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.