Properties

Label 912.d
Number of curves $2$
Conductor $912$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 912.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
912.d1 912f2 \([0, -1, 0, -70245, 7189389]\) \(-9358714467168256/22284891\) \(-91278913536\) \([]\) \(2400\) \(1.3446\)  
912.d2 912f1 \([0, -1, 0, 315, 2349]\) \(841232384/1121931\) \(-4595429376\) \([]\) \(480\) \(0.53984\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 912.d have rank \(1\).

Complex multiplication

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

Modular form 912.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.