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Properties

Label 129430.m
Number of curves $2$
Conductor $129430$
CM no
Rank $2$
Graph

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

Elliptic curves in class 129430.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129430.m1 129430p2 \([1, 1, 1, -9520, 749457]\) \(-51606035560969/102760448000\) \(-190004068352000\) \([]\) \(483840\) \(1.4293\)  
129430.m2 129430p1 \([1, 1, 1, 1015, -21705]\) \(62540044391/150590720\) \(-278442241280\) \([]\) \(161280\) \(0.87997\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 129430.m have rank \(2\).

Complex multiplication

The elliptic curves in class 129430.m do not have complex multiplication.

Modular form 129430.2.a.m

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.