Properties

Label 271040.fh
Number of curves $2$
Conductor $271040$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fh1")
 
E.isogeny_class()
 

Elliptic curves in class 271040.fh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271040.fh1 271040fh1 \([0, 1, 0, -27265, -1745537]\) \(-584043889/1400\) \(-5373270425600\) \([]\) \(663552\) \(1.3221\) \(\Gamma_0(N)\)-optimal
271040.fh2 271040fh2 \([0, 1, 0, 50175, -8730625]\) \(3639707951/10718750\) \(-41139101696000000\) \([]\) \(1990656\) \(1.8714\)  

Rank

sage: E.rank()
 

The elliptic curves in class 271040.fh have rank \(0\).

Complex multiplication

The elliptic curves in class 271040.fh do not have complex multiplication.

Modular form 271040.2.a.fh

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} - 2 q^{9} - 5 q^{13} + q^{15} + 6 q^{17} + 5 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.