Properties

Label 338130.m
Number of curves $2$
Conductor $338130$
CM no
Rank $0$
Graph

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

Elliptic curves in class 338130.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
338130.m1 338130m2 \([1, -1, 0, -119700, 14309406]\) \(10779215329/1232010\) \(21678802533710010\) \([2]\) \(3194880\) \(1.8669\)  
338130.m2 338130m1 \([1, -1, 0, 10350, 1122336]\) \(6967871/35100\) \(-617629701815100\) \([2]\) \(1597440\) \(1.5203\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 338130.m have rank \(0\).

Complex multiplication

The elliptic curves in class 338130.m do not have complex multiplication.

Modular form 338130.2.a.m

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