Properties

Label 30400bv
Number of curves $3$
Conductor $30400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30400bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30400.br3 30400bv1 \([0, -1, 0, 67, -13]\) \(32768/19\) \(-19000000\) \([]\) \(5184\) \(0.086119\) \(\Gamma_0(N)\)-optimal
30400.br2 30400bv2 \([0, -1, 0, -933, 11987]\) \(-89915392/6859\) \(-6859000000\) \([]\) \(15552\) \(0.63543\)  
30400.br1 30400bv3 \([0, -1, 0, -76933, 8238987]\) \(-50357871050752/19\) \(-19000000\) \([]\) \(46656\) \(1.1847\)  

Rank

sage: E.rank()
 

The elliptic curves in class 30400bv have rank \(1\).

Complex multiplication

The elliptic curves in class 30400bv do not have complex multiplication.

Modular form 30400.2.a.bv

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.