Properties

Label 50575.t
Number of curves $3$
Conductor $50575$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 50575.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50575.t1 50575m3 \([0, 1, 1, -948883, -372481731]\) \(-250523582464/13671875\) \(-5156341033935546875\) \([]\) \(725760\) \(2.3488\)  
50575.t2 50575m1 \([0, 1, 1, -9633, 400519]\) \(-262144/35\) \(-13200233046875\) \([]\) \(80640\) \(1.2502\) \(\Gamma_0(N)\)-optimal
50575.t3 50575m2 \([0, 1, 1, 62617, -1008356]\) \(71991296/42875\) \(-16170285482421875\) \([]\) \(241920\) \(1.7995\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50575.t have rank \(0\).

Complex multiplication

The elliptic curves in class 50575.t do not have complex multiplication.

Modular form 50575.2.a.t

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