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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 84150.cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84150.cu1 | 84150cr2 | \([1, -1, 0, -161799417, 789213525741]\) | \(41125104693338423360329/179205840000000000\) | \(2041266521250000000000000\) | \([2]\) | \(19169280\) | \(3.5176\) | |
84150.cu2 | 84150cr1 | \([1, -1, 0, -5127417, 24497493741]\) | \(-1308796492121439049/22000592486400000\) | \(-250600498790400000000000\) | \([2]\) | \(9584640\) | \(3.1711\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 84150.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 84150.cu do not have complex multiplication.Modular form 84150.2.a.cu
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.