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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 174.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
174.c1 | 174d3 | \([1, 0, 1, -310, -2122]\) | \(3279392280793/4698\) | \(4698\) | \([2]\) | \(40\) | \(-0.024261\) | |
174.c2 | 174d4 | \([1, 0, 1, -50, 86]\) | \(13430356633/4243686\) | \(4243686\) | \([2]\) | \(40\) | \(-0.024261\) | |
174.c3 | 174d2 | \([1, 0, 1, -20, -34]\) | \(822656953/30276\) | \(30276\) | \([2, 2]\) | \(20\) | \(-0.37083\) | |
174.c4 | 174d1 | \([1, 0, 1, 0, -2]\) | \(12167/1392\) | \(-1392\) | \([2]\) | \(10\) | \(-0.71741\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 174.c have rank \(0\).
Complex multiplication
The elliptic curves in class 174.c do not have complex multiplication.Modular form 174.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.