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SageMath
E = EllipticCurve("jy1")
E.isogeny_class()
Elliptic curves in class 463680.jy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.jy1 | 463680jy2 | \([0, 0, 0, -14469132, -15402627056]\) | \(1753007192038126081/478174101507200\) | \(91380493844152005427200\) | \([2]\) | \(41287680\) | \(3.1136\) | |
463680.jy2 | 463680jy1 | \([0, 0, 0, -5253132, 4441264144]\) | \(83890194895342081/3958384640000\) | \(756459084856688640000\) | \([2]\) | \(20643840\) | \(2.7670\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 463680.jy have rank \(1\).
Complex multiplication
The elliptic curves in class 463680.jy do not have complex multiplication.Modular form 463680.2.a.jy
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 LMFDB 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 LMFDB labels.