Properties

Label 1216.g
Number of curves $2$
Conductor $1216$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1216.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1216.g1 1216j2 \([0, -1, 0, -4481, 129313]\) \(-37966934881/4952198\) \(-1298188992512\) \([]\) \(1920\) \(1.0575\)  
1216.g2 1216j1 \([0, -1, 0, -1, -607]\) \(-1/608\) \(-159383552\) \([]\) \(384\) \(0.25279\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1216.g have rank \(0\).

Complex multiplication

The elliptic curves in class 1216.g do not have complex multiplication.

Modular form 1216.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4q^{5} - 3q^{7} - 2q^{9} + 2q^{11} + q^{13} - 4q^{15} + 3q^{17} - q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.