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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 8008.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8008.d1 | 8008e2 | \([0, 0, 0, -251, -1290]\) | \(853915554/143143\) | \(293156864\) | \([2]\) | \(1664\) | \(0.34574\) | |
| 8008.d2 | 8008e1 | \([0, 0, 0, 29, -114]\) | \(2634012/7007\) | \(-7175168\) | \([2]\) | \(832\) | \(-0.00083038\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8008.d have rank \(0\).
Complex multiplication
The elliptic curves in class 8008.d do not have complex multiplication.Modular form 8008.2.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.
