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Properties

Label 1274.d
Number of curves $3$
Conductor $1274$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 1274.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1274.d1 1274c3 \([1, 1, 0, -22516, 1291088]\) \(-10730978619193/6656\) \(-783071744\) \([]\) \(2268\) \(1.0273\)  
1274.d2 1274c2 \([1, 1, 0, -221, 2437]\) \(-10218313/17576\) \(-2067798824\) \([]\) \(756\) \(0.47804\)  
1274.d3 1274c1 \([1, 1, 0, 24, -62]\) \(12167/26\) \(-3058874\) \([]\) \(252\) \(-0.071271\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1274.d have rank \(0\).

Complex multiplication

The elliptic curves in class 1274.d do not have complex multiplication.

Modular form 1274.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{8} - 2 q^{9} - 3 q^{10} + 6 q^{11} - q^{12} - q^{13} - 3 q^{15} + q^{16} + 3 q^{17} + 2 q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.