Properties

Label 912.l
Number of curves $2$
Conductor $912$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 912.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
912.l1 912d1 \([0, 1, 0, -16, -28]\) \(470596/57\) \(58368\) \([2]\) \(160\) \(-0.35492\) \(\Gamma_0(N)\)-optimal
912.l2 912d2 \([0, 1, 0, 24, -108]\) \(715822/3249\) \(-6653952\) \([2]\) \(320\) \(-0.0083494\)  

Rank

sage: E.rank()
 

The elliptic curves in class 912.l have rank \(0\).

Complex multiplication

The elliptic curves in class 912.l do not have complex multiplication.

Modular form 912.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4 q^{5} - 4 q^{7} + q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} + 6 q^{17} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.