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Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 248430h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.h2 248430h1 \([1, 1, 0, 239977, 2412593877]\) \(1225043/2016000\) \(-2515179233415899232000\) \([2]\) \(14376960\) \(2.7854\) \(\Gamma_0(N)\)-optimal
248430.h1 248430h2 \([1, 1, 0, -25596743, 48758502213]\) \(1486618221997/36750000\) \(45849621442477329750000\) \([2]\) \(28753920\) \(3.1319\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 248430.2.a.h

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