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Properties

Label 11154m
Number of curves $2$
Conductor $11154$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 11154m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11154.q1 11154m1 \([1, 0, 1, -975873773, 11746188793640]\) \(-21293376668673906679951249/26211168887701209984\) \(-126516305887676189661661056\) \([]\) \(5927040\) \(3.9183\) \(\Gamma_0(N)\)-optimal
11154.q2 11154m2 \([1, 0, 1, 2763672037, -737190761547940]\) \(483641001192506212470106511/48918776756543177755473774\) \(-236121591917473419278720611607166\) \([]\) \(41489280\) \(4.8913\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11154m have rank \(0\).

Complex multiplication

The elliptic curves in class 11154m do not have complex multiplication.

Modular form 11154.2.a.m

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