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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 189618bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.b2 | 189618bj1 | \([1, 1, 0, -69592006, -214810557164]\) | \(7722211175253055152433/340131399900069888\) | \(1641749302220256436027392\) | \([2]\) | \(35043840\) | \(3.4096\) | \(\Gamma_0(N)\)-optimal |
189618.b1 | 189618bj2 | \([1, 1, 0, -187270086, 703054931220]\) | \(150476552140919246594353/42832838728685592576\) | \(206745931471168176416169984\) | \([2]\) | \(70087680\) | \(3.7561\) |
Rank
sage: E.rank()
The elliptic curves in class 189618bj have rank \(0\).
Complex multiplication
The elliptic curves in class 189618bj do not have complex multiplication.Modular form 189618.2.a.bj
sage: E.q_eigenform(10)
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.