Properties

Label 10304.h
Number of curves $2$
Conductor $10304$
CM no
Rank $1$
Graph

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

Elliptic curves in class 10304.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.h1 10304ba1 \([0, 1, 0, -28, -66]\) \(39304000/1127\) \(72128\) \([2]\) \(768\) \(-0.28960\) \(\Gamma_0(N)\)-optimal
10304.h2 10304ba2 \([0, 1, 0, 7, -185]\) \(8000/3703\) \(-15167488\) \([2]\) \(1536\) \(0.056976\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10304.h have rank \(1\).

Complex multiplication

The elliptic curves in class 10304.h do not have complex multiplication.

Modular form 10304.2.a.h

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - q^{7} + q^{9} + 4q^{11} - 2q^{13} - 4q^{19} + O(q^{20})\)  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.