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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1134.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1134.d1 | 1134c2 | \([1, -1, 0, -663, -16867]\) | \(-60698457/200704\) | \(-106662334464\) | \([]\) | \(1728\) | \(0.80236\) | |
1134.d2 | 1134c1 | \([1, -1, 0, 72, 528]\) | \(505636983/1882384\) | \(-152473104\) | \([3]\) | \(576\) | \(0.25305\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1134.d have rank \(0\).
Complex multiplication
The elliptic curves in class 1134.d do not have complex multiplication.Modular form 1134.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.