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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 84150.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84150.x1 | 84150cj2 | \([1, -1, 0, -41783067, 103966210341]\) | \(708234550511150304361/23696640000\) | \(269919540000000000\) | \([2]\) | \(5406720\) | \(2.8443\) | |
84150.x2 | 84150cj1 | \([1, -1, 0, -2615067, 1620226341]\) | \(173629978755828841/1000026931200\) | \(11390931763200000000\) | \([2]\) | \(2703360\) | \(2.4978\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 84150.x have rank \(1\).
Complex multiplication
The elliptic curves in class 84150.x do not have complex multiplication.Modular form 84150.2.a.x
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.