Properties

Label 78400ib
Number of curves $2$
Conductor $78400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ib1")
 
E.isogeny_class()
 

Elliptic curves in class 78400ib

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.js2 78400ib1 \([0, -1, 0, -1633, -1396863]\) \(-4/7\) \(-843308032000000\) \([2]\) \(245760\) \(1.5430\) \(\Gamma_0(N)\)-optimal
78400.js1 78400ib2 \([0, -1, 0, -197633, -33344863]\) \(3543122/49\) \(11806312448000000\) \([2]\) \(491520\) \(1.8896\)  

Rank

sage: E.rank()
 

The elliptic curves in class 78400ib have rank \(1\).

Complex multiplication

The elliptic curves in class 78400ib do not have complex multiplication.

Modular form 78400.2.a.ib

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{9} - 2 q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.