Properties

Label 91035.m
Number of curves $2$
Conductor $91035$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 91035.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.m1 91035y2 \([1, -1, 1, -1556753, 610277186]\) \(23711636464489/4590075735\) \(80768293661446608735\) \([2]\) \(2654208\) \(2.5369\)  
91035.m2 91035y1 \([1, -1, 1, 198922, 56186156]\) \(49471280711/106269975\) \(-1869957064705074975\) \([2]\) \(1327104\) \(2.1903\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 91035.m have rank \(1\).

Complex multiplication

The elliptic curves in class 91035.m do not have complex multiplication.

Modular form 91035.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + q^{7} + 3 q^{8} + q^{10} - 4 q^{11} - 4 q^{13} - q^{14} - q^{16} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.