Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1980.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1980.d1 | 1980e2 | \([0, 0, 0, -3567, 81974]\) | \(26894628304/9075\) | \(1693612800\) | \([2]\) | \(1536\) | \(0.74298\) | |
1980.d2 | 1980e1 | \([0, 0, 0, -192, 1649]\) | \(-67108864/61875\) | \(-721710000\) | \([2]\) | \(768\) | \(0.39640\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1980.d have rank \(1\).
Complex multiplication
The elliptic curves in class 1980.d do not have complex multiplication.Modular form 1980.2.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.