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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 80016.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80016.d1 | 80016c1 | \([0, 1, 0, -1624, 24596]\) | \(115714886617/320064\) | \(1310982144\) | \([2]\) | \(36864\) | \(0.62234\) | \(\Gamma_0(N)\)-optimal |
80016.d2 | 80016c2 | \([0, 1, 0, -984, 44820]\) | \(-25750777177/200080008\) | \(-819527712768\) | \([2]\) | \(73728\) | \(0.96891\) |
Rank
sage: E.rank()
The elliptic curves in class 80016.d have rank \(1\).
Complex multiplication
The elliptic curves in class 80016.d do not have complex multiplication.Modular form 80016.2.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.