Properties

Label 3822.h
Number of curves $4$
Conductor $3822$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3822.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.h1 3822d3 \([1, 1, 0, -95869, -11462975]\) \(828279937799497/193444524\) \(22758554804076\) \([2]\) \(18432\) \(1.5536\)  
3822.h2 3822d2 \([1, 1, 0, -6689, -137115]\) \(281397674377/96589584\) \(11363667968016\) \([2, 2]\) \(9216\) \(1.2070\)  
3822.h3 3822d1 \([1, 1, 0, -2769, 53397]\) \(19968681097/628992\) \(74000279808\) \([2]\) \(4608\) \(0.86045\) \(\Gamma_0(N)\)-optimal
3822.h4 3822d4 \([1, 1, 0, 19771, -925623]\) \(7264187703863/7406095788\) \(-871319763362412\) \([2]\) \(18432\) \(1.5536\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3822.h have rank \(0\).

Complex multiplication

The elliptic curves in class 3822.h do not have complex multiplication.

Modular form 3822.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} - q^{8} + q^{9} - 2 q^{10} - 4 q^{11} - q^{12} - q^{13} - 2 q^{15} + q^{16} + 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.