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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1083d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1083.b2 | 1083d1 | \([1, 0, 0, 2, -1]\) | \(2375/3\) | \(-1083\) | \([]\) | \(36\) | \(-0.73170\) | \(\Gamma_0(N)\)-optimal |
1083.b1 | 1083d2 | \([1, 0, 0, -663, 6516]\) | \(-89289015625/2187\) | \(-789507\) | \([]\) | \(252\) | \(0.24125\) |
Rank
sage: E.rank()
The elliptic curves in class 1083d have rank \(1\).
Complex multiplication
The elliptic curves in class 1083d do not have complex multiplication.Modular form 1083.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.