Properties

Label 53361u
Number of curves $2$
Conductor $53361$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 53361u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53361.cd2 53361u1 \([0, 0, 1, -124509, 18375453]\) \(-28672/3\) \(-22335167517477507\) \([]\) \(470400\) \(1.8761\) \(\Gamma_0(N)\)-optimal
53361.cd1 53361u2 \([0, 0, 1, -48683019, -130846808997]\) \(-1713910976512/1594323\) \(-11869823760655763797587\) \([]\) \(6115200\) \(3.1586\)  

Rank

sage: E.rank()
 

The elliptic curves in class 53361u have rank \(1\).

Complex multiplication

The elliptic curves in class 53361u do not have complex multiplication.

Modular form 53361.2.a.u

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 4 q^{10} - q^{13} - 4 q^{16} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.