Properties

Label 4275.i
Number of curves $3$
Conductor $4275$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4275.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4275.i1 4275k3 \([0, 0, 1, -173100, 27720031]\) \(-50357871050752/19\) \(-216421875\) \([]\) \(7776\) \(1.3875\)  
4275.i2 4275k2 \([0, 0, 1, -2100, 39406]\) \(-89915392/6859\) \(-78128296875\) \([]\) \(2592\) \(0.83816\)  
4275.i3 4275k1 \([0, 0, 1, 150, 31]\) \(32768/19\) \(-216421875\) \([]\) \(864\) \(0.28885\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4275.i have rank \(1\).

Complex multiplication

The elliptic curves in class 4275.i do not have complex multiplication.

Modular form 4275.2.a.i

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.