Properties

Label 22848.h
Number of curves $4$
Conductor $22848$
CM no
Rank $1$
Graph

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

Elliptic curves in class 22848.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.h1 22848b4 \([0, -1, 0, -5089, -138047]\) \(444893916104/9639\) \(315850752\) \([2]\) \(14336\) \(0.74729\)  
22848.h2 22848b2 \([0, -1, 0, -329, -1911]\) \(964430272/127449\) \(522031104\) \([2, 2]\) \(7168\) \(0.40071\)  
22848.h3 22848b1 \([0, -1, 0, -84, 294]\) \(1036433728/122451\) \(7836864\) \([2]\) \(3584\) \(0.054141\) \(\Gamma_0(N)\)-optimal
22848.h4 22848b3 \([0, -1, 0, 511, -10815]\) \(449455096/1753941\) \(-57473138688\) \([2]\) \(14336\) \(0.74729\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22848.h have rank \(1\).

Complex multiplication

The elliptic curves in class 22848.h do not have complex multiplication.

Modular form 22848.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{5} - q^{7} + q^{9} + 2q^{13} + 2q^{15} - q^{17} + 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.