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Properties

Label 56350o
Number of curves $2$
Conductor $56350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 56350o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56350.u2 56350o1 \([1, 0, 1, 44900389, 129134392678]\) \(3403656999841015798655/4418852112356605952\) \(-12996838304166058341171200\) \([]\) \(10450944\) \(3.5048\) \(\Gamma_0(N)\)-optimal
56350.u1 56350o2 \([1, 0, 1, -1276610011, 17662577879398]\) \(-78229436189152112196207745/549794097750525813248\) \(-1617068145156290285070348800\) \([]\) \(31352832\) \(4.0541\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56350o have rank \(1\).

Complex multiplication

The elliptic curves in class 56350o do not have complex multiplication.

Modular form 56350.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} - 2 q^{9} + 3 q^{11} + q^{12} + 2 q^{13} + q^{16} + 3 q^{17} + 2 q^{18} - 5 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.