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Properties

Label 230115.y
Number of curves $2$
Conductor $230115$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 230115.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
230115.y1 230115y1 \([1, 0, 1, -197593, -33820969]\) \(5763259856089/450225\) \(66649458125025\) \([2]\) \(912384\) \(1.6998\) \(\Gamma_0(N)\)-optimal
230115.y2 230115y2 \([1, 0, 1, -184368, -38539649]\) \(-4681768588489/1621620405\) \(-240058018274715045\) \([2]\) \(1824768\) \(2.0463\)  

Rank

sage: E.rank()
 

The elliptic curves in class 230115.y have rank \(1\).

Complex multiplication

The elliptic curves in class 230115.y do not have complex multiplication.

Modular form 230115.2.a.y

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