Properties

Label 47915.b
Number of curves $3$
Conductor $47915$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47915.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47915.b1 47915c3 \([0, 1, 1, -179795, -30756119]\) \(-250523582464/13671875\) \(-35078290748046875\) \([]\) \(311040\) \(1.9329\)  
47915.b2 47915c1 \([0, 1, 1, -1825, 32691]\) \(-262144/35\) \(-89800424315\) \([]\) \(34560\) \(0.83431\) \(\Gamma_0(N)\)-optimal
47915.b3 47915c2 \([0, 1, 1, 11865, -80936]\) \(71991296/42875\) \(-110005519785875\) \([]\) \(103680\) \(1.3836\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47915.b have rank \(1\).

Complex multiplication

The elliptic curves in class 47915.b do not have complex multiplication.

Modular form 47915.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{4} + q^{5} + q^{7} - 2q^{9} - 3q^{11} - 2q^{12} - 5q^{13} + q^{15} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})\)  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.