Properties

Label 248430i
Number of curves $2$
Conductor $248430$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 248430i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.i1 248430i1 \([1, 1, 0, -313291423, -2133269200187]\) \(13156820005959211457413/8823316631734080\) \(2280605469359921463090240\) \([2]\) \(92897280\) \(3.6124\) \(\Gamma_0(N)\)-optimal
248430.i2 248430i2 \([1, 1, 0, -252113943, -2991234415203]\) \(-6856397880127437095173/10985435736872272200\) \(-2839458887229007236670986600\) \([2]\) \(185794560\) \(3.9589\)  

Rank

sage: E.rank()
 

The elliptic curves in class 248430i have rank \(1\).

Complex multiplication

The elliptic curves in class 248430i do not have complex multiplication.

Modular form 248430.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - 2 q^{11} - q^{12} + q^{15} + q^{16} - 6 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.