Properties

Label 129430.t
Number of curves $2$
Conductor $129430$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 129430.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129430.t1 129430r1 \([1, 1, 1, -60, -205]\) \(-12932809/70\) \(-129430\) \([]\) \(25704\) \(-0.17502\) \(\Gamma_0(N)\)-optimal
129430.t2 129430r2 \([1, 1, 1, 155, -893]\) \(222641831/343000\) \(-634207000\) \([]\) \(77112\) \(0.37429\)  

Rank

sage: E.rank()
 

The elliptic curves in class 129430.t have rank \(0\).

Complex multiplication

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

Modular form 129430.2.a.t

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