Properties

Label 4275.h
Number of curves $2$
Conductor $4275$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4275.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4275.h1 4275l2 \([1, -1, 1, -17105, 47022]\) \(48587168449/28048275\) \(319487382421875\) \([2]\) \(15360\) \(1.4727\)  
4275.h2 4275l1 \([1, -1, 1, 4270, 4272]\) \(756058031/438615\) \(-4996098984375\) \([2]\) \(7680\) \(1.1261\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4275.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 2 q^{7} + 3 q^{8} + 6 q^{11} - 2 q^{14} - q^{16} - 6 q^{17} + q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.