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Properties

Label 3648.h
Number of curves $2$
Conductor $3648$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3648.h

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3648.h1 3648f2 \([0, -1, 0, -17561, -889893]\) \(-9358714467168256/22284891\) \(-1426233024\) \([]\) \(4800\) \(0.99798\)  
3648.h2 3648f1 \([0, -1, 0, 79, -333]\) \(841232384/1121931\) \(-71803584\) \([]\) \(960\) \(0.19326\) \(\Gamma_0(N)\)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 3648.h have rank \(0\).

Complex multiplication

The elliptic curves in class 3648.h do not have complex multiplication.

Modular form 3648.2.a.h

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + 3 q^{7} + q^{9} + 3 q^{11} + 6 q^{13} + q^{15} + 3 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.