↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 294.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
294.e1 294a2 \([1, 1, 1, -6910, -232261]\) \(-6329617441/279936\) \(-1613775332736\) \([]\) \(588\) \(1.1074\)  
294.e2 294a1 \([1, 1, 1, -50, 293]\) \(-2401/6\) \(-34588806\) \([]\) \(84\) \(0.13448\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 294.2.a.e

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.