Properties

Label 174.e
Number of curves 2
Conductor 174
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("174.e1")
sage: E.isogeny_class()

Elliptic curves in class 174.e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
174.e1 174b2 [1, 0, 0, -6511, -203353] 1 196  
174.e2 174b1 [1, 0, 0, -1, 137] 7 28 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 174.e have rank \(0\).

Modular form 174.2.a.e

sage: E.q_eigenform(10)
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 2q^{11} + q^{12} + q^{14} - q^{15} + q^{16} - 3q^{17} + q^{18} - q^{19} + O(q^{20}) \)

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.