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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 139230.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139230.o1 | 139230ek2 | \([1, -1, 0, -14820, 608400]\) | \(13332790119579867/1865238939200\) | \(50361451358400\) | \([2]\) | \(491520\) | \(1.3555\) | |
139230.o2 | 139230ek1 | \([1, -1, 0, 1500, 50256]\) | \(13818816647973/49012920320\) | \(-1323348848640\) | \([2]\) | \(245760\) | \(1.0089\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139230.o have rank \(2\).
Complex multiplication
The elliptic curves in class 139230.o do not have complex multiplication.Modular form 139230.2.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.