Properties

Label 31200.bh
Number of curves $4$
Conductor $31200$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31200.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.bh1 31200p4 \([0, 1, 0, -5688008, -5221701012]\) \(2543984126301795848/909361981125\) \(7274895849000000000\) \([2]\) \(1179648\) \(2.5885\)  
31200.bh2 31200p3 \([0, 1, 0, -2938008, 1897486488]\) \(350584567631475848/8259273550125\) \(66074188401000000000\) \([2]\) \(1179648\) \(2.5885\)  
31200.bh3 31200p1 \([0, 1, 0, -406758, -56638512]\) \(7442744143086784/2927948765625\) \(2927948765625000000\) \([2, 2]\) \(589824\) \(2.2419\) \(\Gamma_0(N)\)-optimal
31200.bh4 31200p2 \([0, 1, 0, 1304367, -407419137]\) \(3834800837445824/3342041015625\) \(-213890625000000000000\) \([2]\) \(1179648\) \(2.5885\)  

Rank

sage: E.rank()
 

The elliptic curves in class 31200.bh have rank \(0\).

Complex multiplication

The elliptic curves in class 31200.bh do not have complex multiplication.

Modular form 31200.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4q^{7} + q^{9} - q^{13} - 2q^{17} + 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.