Properties

Label 141570eb
Number of curves $3$
Conductor $141570$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eb1")
 
E.isogeny_class()
 

Elliptic curves in class 141570eb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141570.r2 141570eb1 \([1, -1, 0, -530910, 209605050]\) \(-12814546750201/7261718750\) \(-9378277165511718750\) \([]\) \(3110400\) \(2.3435\) \(\Gamma_0(N)\)-optimal
141570.r3 141570eb2 \([1, -1, 0, 4233465, -2823396075]\) \(6497225437879799/6424482779000\) \(-8297013726470605851000\) \([]\) \(9331200\) \(2.8928\)  
141570.r1 141570eb3 \([1, -1, 0, -101590110, -397941939180]\) \(-89783052551043953401/1020142489034240\) \(-1317481348403654704258560\) \([]\) \(27993600\) \(3.4421\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141570eb have rank \(1\).

Complex multiplication

The elliptic curves in class 141570eb do not have complex multiplication.

Modular form 141570.2.a.eb

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.