Properties

Label 101430.r
Number of curves $2$
Conductor $101430$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 101430.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.r1 101430t2 \([1, -1, 0, -156183750, -751241073164]\) \(-11795263402880796810182449/404296875000000\) \(-14441888671875000000\) \([]\) \(10575360\) \(3.1745\)  
101430.r2 101430t1 \([1, -1, 0, -1778310, -1197034700]\) \(-17410957409801706289/7266093465600000\) \(-259552124684697600000\) \([]\) \(3525120\) \(2.6252\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 101430.r have rank \(1\).

Complex multiplication

The elliptic curves in class 101430.r do not have complex multiplication.

Modular form 101430.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 2 q^{13} + q^{16} + 3 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.