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Properties

Label 248430.u
Number of curves $2$
Conductor $248430$
CM no
Rank $0$
Graph

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

Elliptic curves in class 248430.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.u1 248430u1 \([1, 1, 0, -208399818, -976079715372]\) \(5138936454608263/861237411840\) \(167751093997718464804945920\) \([2]\) \(132464640\) \(3.7531\) \(\Gamma_0(N)\)-optimal
248430.u2 248430u2 \([1, 1, 0, 385182262, -5519475672108]\) \(32447412812909177/86348722636800\) \(-16818931096690195786486118400\) \([2]\) \(264929280\) \(4.0997\)  

Rank

sage: E.rank()
 

The elliptic curves in class 248430.u have rank \(0\).

Complex multiplication

The elliptic curves in class 248430.u do not have complex multiplication.

Modular form 248430.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} + 2 q^{11} - q^{12} + q^{15} + q^{16} - q^{18} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.