Properties

Label 3648g
Number of curves $4$
Conductor $3648$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3648g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3648.o3 3648g1 \([0, -1, 0, -97, -287]\) \(389017/57\) \(14942208\) \([2]\) \(768\) \(0.10156\) \(\Gamma_0(N)\)-optimal
3648.o2 3648g2 \([0, -1, 0, -417, 3105]\) \(30664297/3249\) \(851705856\) \([2, 2]\) \(1536\) \(0.44814\)  
3648.o1 3648g3 \([0, -1, 0, -6497, 203745]\) \(115714886617/1539\) \(403439616\) \([2]\) \(3072\) \(0.79471\)  
3648.o4 3648g4 \([0, -1, 0, 543, 14433]\) \(67419143/390963\) \(-102488604672\) \([2]\) \(3072\) \(0.79471\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3648.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} + q^{9} - 6 q^{13} - 2 q^{15} - 6 q^{17} + q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.