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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1274c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1274.d3 | 1274c1 | \([1, 1, 0, 24, -62]\) | \(12167/26\) | \(-3058874\) | \([]\) | \(252\) | \(-0.071271\) | \(\Gamma_0(N)\)-optimal |
1274.d2 | 1274c2 | \([1, 1, 0, -221, 2437]\) | \(-10218313/17576\) | \(-2067798824\) | \([]\) | \(756\) | \(0.47804\) | |
1274.d1 | 1274c3 | \([1, 1, 0, -22516, 1291088]\) | \(-10730978619193/6656\) | \(-783071744\) | \([]\) | \(2268\) | \(1.0273\) |
Rank
sage: E.rank()
The elliptic curves in class 1274c have rank \(0\).
Complex multiplication
The elliptic curves in class 1274c do not have complex multiplication.Modular form 1274.2.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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.