Properties

Label 15400m
Number of curves $2$
Conductor $15400$
CM no
Rank $0$
Graph

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

Elliptic curves in class 15400m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15400.b2 15400m1 \([0, 1, 0, 95692, 12109888]\) \(24226243449392/29774625727\) \(-119098502908000000\) \([2]\) \(122880\) \(1.9627\) \(\Gamma_0(N)\)-optimal
15400.b1 15400m2 \([0, 1, 0, -569808, 115927888]\) \(1278763167594532/375974556419\) \(6015592902704000000\) \([2]\) \(245760\) \(2.3092\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15400m have rank \(0\).

Complex multiplication

The elliptic curves in class 15400m do not have complex multiplication.

Modular form 15400.2.a.m

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{7} + q^{9} - q^{11} - 4 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.