Properties

Label 1575.h
Number of curves $4$
Conductor $1575$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 1575.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1575.h1 1575f3 \([1, -1, 0, -25317, 1556716]\) \(157551496201/13125\) \(149501953125\) \([2]\) \(3072\) \(1.1881\)  
1575.h2 1575f2 \([1, -1, 0, -1692, 21091]\) \(47045881/11025\) \(125581640625\) \([2, 2]\) \(1536\) \(0.84149\)  
1575.h3 1575f1 \([1, -1, 0, -567, -4784]\) \(1771561/105\) \(1196015625\) \([2]\) \(768\) \(0.49492\) \(\Gamma_0(N)\)-optimal
1575.h4 1575f4 \([1, -1, 0, 3933, 127966]\) \(590589719/972405\) \(-11076300703125\) \([2]\) \(3072\) \(1.1881\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1575.h have rank \(0\).

Complex multiplication

The elliptic curves in class 1575.h do not have complex multiplication.

Modular form 1575.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - q^{7} - 3q^{8} + 6q^{13} - q^{14} - q^{16} + 2q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.