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Properties

Label 155298.u
Number of curves $2$
Conductor $155298$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 155298.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155298.u1 155298m2 \([1, 1, 1, -1149883, -278100151]\) \(168145285832097029016625/64010574495618296832\) \(64010574495618296832\) \([2]\) \(3778560\) \(2.4998\)  
155298.u2 155298m1 \([1, 1, 1, -1011643, -391954615]\) \(114500024963059155864625/36780823085580288\) \(36780823085580288\) \([2]\) \(1889280\) \(2.1532\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 155298.u have rank \(0\).

Complex multiplication

The elliptic curves in class 155298.u do not have complex multiplication.

Modular form 155298.2.a.u

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.