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Properties

Label 400192.u
Number of curves $2$
Conductor $400192$
CM no
Rank $0$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 400192.u have rank \(0\).

Complex multiplication

The elliptic curves in class 400192.u do not have complex multiplication.

Modular form 400192.2.a.u

Copy content sage:E.q_eigenform(10)
 
\(q + q^{5} - 4 q^{7} - 3 q^{9} - 3 q^{11} - 4 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 400192.u

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
400192.u1 400192u1 \([0, 0, 0, -3452332, -2468976432]\) \(-607782291676209/74\) \(-554045014016\) \([]\) \(3354624\) \(2.1163\) \(\Gamma_0(N)\)-optimal*
400192.u2 400192u2 \([0, 0, 0, 6931028, -12699181872]\) \(4918167786495951/12151280273024\) \(-90977787151080086306816\) \([]\) \(23482368\) \(3.0893\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 400192.u1.