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Properties

Label 143430.u
Number of curves $3$
Conductor $143430$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 143430.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
143430.u1 143430b3 \([1, 0, 0, -25739105055, -1892948058681663]\) \(-1885836510340587452798601371917380721/456620935285821819761620060937640\) \(-456620935285821819761620060937640\) \([]\) \(786060288\) \(4.9853\)  
143430.u2 143430b1 \([1, 0, 0, -505833255, 4487049903177]\) \(-14313500104002032435046925025521/414610368065961984000000000\) \(-414610368065961984000000000\) \([9]\) \(87340032\) \(3.8867\) \(\Gamma_0(N)\)-optimal
143430.u3 143430b2 \([1, 0, 0, 2284886745, 17553247599177]\) \(1319221579871651050877529633054479/896541855128180128429337664000\) \(-896541855128180128429337664000\) \([3]\) \(262020096\) \(4.4360\)  

Rank

sage: E.rank()
 

The elliptic curves in class 143430.u have rank \(1\).

Complex multiplication

The elliptic curves in class 143430.u do not have complex multiplication.

Modular form 143430.2.a.u

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.