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Properties

Label 279312.u
Number of curves $2$
Conductor $279312$
CM no
Rank $1$
Graph

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

Elliptic curves in class 279312.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
279312.u1 279312u2 \([0, -1, 0, -1418, -20085]\) \(37280608000/3993\) \(33796752\) \([]\) \(124416\) \(0.47533\)  
279312.u2 279312u1 \([0, -1, 0, -38, 63]\) \(736000/297\) \(2513808\) \([]\) \(41472\) \(-0.073976\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 279312.u have rank \(1\).

Complex multiplication

The elliptic curves in class 279312.u do not have complex multiplication.

Modular form 279312.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} - q^{11} + 2 q^{13} + 3 q^{17} + 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.