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Properties

Label 294.a
Number of curves $2$
Conductor $294$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 294.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
294.a1 294e2 \([1, 1, 0, -34864, 2503936]\) \(-16591834777/98304\) \(-27768446877696\) \([]\) \(1260\) \(1.4199\)  
294.a2 294e1 \([1, 1, 0, 1151, 18901]\) \(596183/864\) \(-244058615136\) \([]\) \(420\) \(0.87057\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 294.a have rank \(0\).

Complex multiplication

The elliptic curves in class 294.a do not have complex multiplication.

Modular form 294.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.