Properties

Label 912.c
Number of curves $4$
Conductor $912$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 912.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
912.c1 912e3 \([0, -1, 0, -6848, 220416]\) \(8671983378625/82308\) \(337133568\) \([2]\) \(864\) \(0.79865\)  
912.c2 912e4 \([0, -1, 0, -6688, 231040]\) \(-8078253774625/846825858\) \(-3468598714368\) \([2]\) \(1728\) \(1.1452\)  
912.c3 912e1 \([0, -1, 0, -128, 0]\) \(57066625/32832\) \(134479872\) \([2]\) \(288\) \(0.24934\) \(\Gamma_0(N)\)-optimal
912.c4 912e2 \([0, -1, 0, 512, -512]\) \(3616805375/2105352\) \(-8623521792\) \([2]\) \(576\) \(0.59592\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 912.2.a.c

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.