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Properties

Label 462462bl
Number of curves $2$
Conductor $462462$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 462462bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462462.bl1 462462bl1 \([1, 1, 0, -34236423652, 2440841417606992]\) \(-21293376668673906679951249/26211168887701209984\) \(-5462994204489432944750449608576\) \([]\) \(1600300800\) \(4.8077\) \(\Gamma_0(N)\)-optimal
462462.bl2 462462bl2 \([1, 1, 0, 96957464558, -153187039748555798]\) \(483641001192506212470106511/48918776756543177755473774\) \(-10195767882641180811891244824899285886\) \([]\) \(11202105600\) \(5.7807\)  

Rank

sage: E.rank()
 

The elliptic curves in class 462462bl have rank \(1\).

Complex multiplication

The elliptic curves in class 462462bl do not have complex multiplication.

Modular form 462462.2.a.bl

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - q^{15} + q^{16} + 4 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.