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Properties

Label 28050m
Number of curves $2$
Conductor $28050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 28050m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28050.r1 28050m1 \([1, 1, 0, -4900, -134000]\) \(832972004929/610368\) \(9537000000\) \([2]\) \(30720\) \(0.84909\) \(\Gamma_0(N)\)-optimal
28050.r2 28050m2 \([1, 1, 0, -3900, -189000]\) \(-420021471169/727634952\) \(-11369296125000\) \([2]\) \(61440\) \(1.1957\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28050m have rank \(1\).

Complex multiplication

The elliptic curves in class 28050m do not have complex multiplication.

Modular form 28050.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + 2 q^{7} - q^{8} + q^{9} + q^{11} - q^{12} - 2 q^{14} + q^{16} + q^{17} - q^{18} + O(q^{20})\) 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.