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Properties

Label 234135.l
Number of curves $2$
Conductor $234135$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 234135.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
234135.l1 234135l2 \([1, -1, 1, -90047, -10341944]\) \(2315685267/9245\) \(322369777081935\) \([2]\) \(1105920\) \(1.6407\)  
234135.l2 234135l1 \([1, -1, 1, -8372, 14446]\) \(1860867/1075\) \(37484857800225\) \([2]\) \(552960\) \(1.2941\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 234135.l have rank \(0\).

Complex multiplication

The elliptic curves in class 234135.l do not have complex multiplication.

Modular form 234135.2.a.l

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.