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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 301530o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301530.o2 | 301530o1 | \([1, 1, 0, 1516368, 919501164]\) | \(2604774197916071/3971299160700\) | \(-587894801739178362300\) | \([2]\) | \(15138816\) | \(2.6706\) | \(\Gamma_0(N)\)-optimal |
301530.o1 | 301530o2 | \([1, 1, 0, -10052862, 9265543686]\) | \(758972300355722809/188464202853750\) | \(27899465814131218233750\) | \([2]\) | \(30277632\) | \(3.0172\) |
Rank
sage: E.rank()
The elliptic curves in class 301530o have rank \(0\).
Complex multiplication
The elliptic curves in class 301530o do not have complex multiplication.Modular form 301530.2.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 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.