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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 35739.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35739.o1 | 35739e2 | \([1, -1, 0, -6024, -177471]\) | \(19034163/121\) | \(153698893227\) | \([2]\) | \(52416\) | \(0.98353\) | |
35739.o2 | 35739e1 | \([1, -1, 0, -609, 1224]\) | \(19683/11\) | \(13972626657\) | \([2]\) | \(26208\) | \(0.63696\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35739.o have rank \(0\).
Complex multiplication
The elliptic curves in class 35739.o do not have complex multiplication.Modular form 35739.2.a.o
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.