Properties

Label 304200f
Number of curves $2$
Conductor $304200$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 304200f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
304200.f2 304200f1 \([0, 0, 0, 177450, -91999375]\) \(702464/4563\) \(-4014006945360750000\) \([2]\) \(5160960\) \(2.2515\) \(\Gamma_0(N)\)-optimal
304200.f1 304200f2 \([0, 0, 0, -2294175, -1216588750]\) \(94875856/9477\) \(133388538491988000000\) \([2]\) \(10321920\) \(2.5980\)  

Rank

sage: E.rank()
 

The elliptic curves in class 304200f have rank \(2\).

Complex multiplication

The elliptic curves in class 304200f do not have complex multiplication.

Modular form 304200.2.a.f

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.