Properties

Label 63075.c
Number of curves $2$
Conductor $63075$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 63075.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63075.c1 63075v1 \([0, 1, 1, -7008, -233806]\) \(-102400/3\) \(-1115293726875\) \([]\) \(134400\) \(1.0905\) \(\Gamma_0(N)\)-optimal
63075.c2 63075v2 \([0, 1, 1, 35042, 11161744]\) \(20480/243\) \(-56461744923046875\) \([]\) \(672000\) \(1.8953\)  

Rank

sage: E.rank()
 

The elliptic curves in class 63075.c have rank \(1\).

Complex multiplication

The elliptic curves in class 63075.c do not have complex multiplication.

Modular form 63075.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{6} - 3 q^{7} + q^{9} - 2 q^{11} + 2 q^{12} + q^{13} + 6 q^{14} - 4 q^{16} - 2 q^{17} - 2 q^{18} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.