Properties

Label 10115.f
Number of curves $3$
Conductor $10115$
CM no
Rank $0$
Graph

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

Elliptic curves in class 10115.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10115.f1 10115g3 \([0, -1, 1, -37955, -2964672]\) \(-250523582464/13671875\) \(-330005826171875\) \([]\) \(30240\) \(1.5441\)  
10115.f2 10115g1 \([0, -1, 1, -385, 3358]\) \(-262144/35\) \(-844814915\) \([]\) \(3360\) \(0.44546\) \(\Gamma_0(N)\)-optimal
10115.f3 10115g2 \([0, -1, 1, 2505, -9069]\) \(71991296/42875\) \(-1034898270875\) \([]\) \(10080\) \(0.99476\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10115.f have rank \(0\).

Complex multiplication

The elliptic curves in class 10115.f do not have complex multiplication.

Modular form 10115.2.a.f

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