Properties

Label 25200bl
Number of curves $4$
Conductor $25200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 25200bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.ep4 25200bl1 \([0, 0, 0, 1950, -273625]\) \(4499456/180075\) \(-32818668750000\) \([2]\) \(49152\) \(1.2734\) \(\Gamma_0(N)\)-optimal
25200.ep3 25200bl2 \([0, 0, 0, -53175, -4518250]\) \(5702413264/275625\) \(803722500000000\) \([2, 2]\) \(98304\) \(1.6199\)  
25200.ep2 25200bl3 \([0, 0, 0, -147675, 15988250]\) \(30534944836/8203125\) \(95681250000000000\) \([2]\) \(196608\) \(1.9665\)  
25200.ep1 25200bl4 \([0, 0, 0, -840675, -296680750]\) \(5633270409316/14175\) \(165337200000000\) \([2]\) \(196608\) \(1.9665\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25200bl have rank \(1\).

Complex multiplication

The elliptic curves in class 25200bl do not have complex multiplication.

Modular form 25200.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{7} + 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.