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Properties

Label 248430.g
Number of curves $2$
Conductor $248430$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 248430.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.g1 248430g2 \([1, 1, 0, -268713, 53502597]\) \(-1533284625258841/1474560\) \(-2063630499840\) \([]\) \(1710720\) \(1.6576\)  
248430.g2 248430g1 \([1, 1, 0, -2538, 107892]\) \(-1292696041/2916000\) \(-4080909924000\) \([]\) \(570240\) \(1.1083\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 248430.g have rank \(0\).

Complex multiplication

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

Modular form 248430.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.