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Properties

Label 110946m
Number of curves $2$
Conductor $110946$
CM no
Rank $0$
Graph

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

Elliptic curves in class 110946m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
110946.p1 110946m1 \([1, 0, 1, -1562525, -751904764]\) \(88818021833113/178596\) \(848349617025636\) \([2]\) \(2150400\) \(2.1158\) \(\Gamma_0(N)\)-optimal
110946.p2 110946m2 \([1, 0, 1, -1545715, -768869416]\) \(-85982176079353/3987066402\) \(-18938981025288810882\) \([2]\) \(4300800\) \(2.4624\)  

Rank

sage: E.rank()
 

The elliptic curves in class 110946m have rank \(0\).

Complex multiplication

The elliptic curves in class 110946m do not have complex multiplication.

Modular form 110946.2.a.m

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.