Properties

Label 5915.f
Number of curves $3$
Conductor $5915$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5915.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5915.f1 5915f3 \([0, 1, 1, -22195, -1338801]\) \(-250523582464/13671875\) \(-65991529296875\) \([]\) \(12312\) \(1.4099\)  
5915.f2 5915f1 \([0, 1, 1, -225, 1369]\) \(-262144/35\) \(-168938315\) \([]\) \(1368\) \(0.31132\) \(\Gamma_0(N)\)-optimal
5915.f3 5915f2 \([0, 1, 1, 1465, -3194]\) \(71991296/42875\) \(-206949435875\) \([]\) \(4104\) \(0.86063\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5915.f have rank \(0\).

Complex multiplication

The elliptic curves in class 5915.f do not have complex multiplication.

Modular form 5915.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{4} + q^{5} - q^{7} - 2q^{9} + 3q^{11} - 2q^{12} + q^{15} + 4q^{16} + 3q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.