Properties

Label 12696.i
Number of curves $2$
Conductor $12696$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12696.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.i1 12696d2 \([0, -1, 0, -605352, 181458540]\) \(80919167474/14283\) \(4330284242098176\) \([2]\) \(101376\) \(2.0052\)  
12696.i2 12696d1 \([0, -1, 0, -34032, 3435228]\) \(-28756228/16767\) \(-2541688576883712\) \([2]\) \(50688\) \(1.6586\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 12696.i have rank \(0\).

Complex multiplication

The elliptic curves in class 12696.i do not have complex multiplication.

Modular form 12696.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.