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Properties

Label 146205i
Number of curves $2$
Conductor $146205$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 146205i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
146205.j2 146205i1 \([1, -1, 0, -609, 179558]\) \(-9/5\) \(-13890061135845\) \([]\) \(217728\) \(1.2009\) \(\Gamma_0(N)\)-optimal
146205.j1 146205i2 \([1, -1, 0, -731634, -241731235]\) \(-15590912409/78125\) \(-217032205247578125\) \([]\) \(1524096\) \(2.1739\)  

Rank

sage: E.rank()
 

The elliptic curves in class 146205i have rank \(0\).

Complex multiplication

The elliptic curves in class 146205i do not have complex multiplication.

Modular form 146205.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} - 3 q^{7} - 3 q^{8} + q^{10} + 2 q^{11} + 2 q^{13} - 3 q^{14} - q^{16} - 4 q^{17} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.