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Properties

Label 110400.h
Number of curves $2$
Conductor $110400$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 110400.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
110400.h1 110400bm2 \([0, -1, 0, -388033, -92864063]\) \(1577505447721/838350\) \(3433881600000000\) \([2]\) \(1327104\) \(1.9308\)  
110400.h2 110400bm1 \([0, -1, 0, -20033, -1968063]\) \(-217081801/285660\) \(-1170063360000000\) \([2]\) \(663552\) \(1.5842\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 110400.h have rank \(0\).

Complex multiplication

The elliptic curves in class 110400.h do not have complex multiplication.

Modular form 110400.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.