Properties

Label 150075bj
Number of curves $2$
Conductor $150075$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 150075bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
150075.bj1 150075bj1 \([1, -1, 0, -84042, -9356009]\) \(5763259856089/450225\) \(5128344140625\) \([2]\) \(331776\) \(1.4861\) \(\Gamma_0(N)\)-optimal
150075.bj2 150075bj2 \([1, -1, 0, -78417, -10666634]\) \(-4681768588489/1621620405\) \(-18471269925703125\) \([2]\) \(663552\) \(1.8326\)  

Rank

sage: E.rank()
 

The elliptic curves in class 150075bj have rank \(2\).

Complex multiplication

The elliptic curves in class 150075bj do not have complex multiplication.

Modular form 150075.2.a.bj

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 3 q^{8} - 2 q^{11} - 2 q^{13} - q^{16} - 4 q^{17} + O(q^{20})\) 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.