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Properties

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

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 155298c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155298.bb1 155298c1 \([1, 0, 0, -11086251, 14206955697]\) \(-150687710990775834204537649/1643007120586850304\) \(-1643007120586850304\) \([7]\) \(6914880\) \(2.6498\) \(\Gamma_0(N)\)-optimal
155298.bb2 155298c2 \([1, 0, 0, 79590489, -217549296723]\) \(55758005550664597131275876111/52714175901876612774649284\) \(-52714175901876612774649284\) \([]\) \(48404160\) \(3.6227\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 155298.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} - q^{13} + q^{14} - q^{15} + q^{16} + 4 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.