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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 150075n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
150075.j2 | 150075n1 | \([0, 0, 1, 5550, -499469]\) | \(1659797504/10421875\) | \(-118711669921875\) | \([]\) | \(350208\) | \(1.3825\) | \(\Gamma_0(N)\)-optimal |
150075.j1 | 150075n2 | \([0, 0, 1, -50700, 14659906]\) | \(-1265319018496/7418524075\) | \(-84501625791796875\) | \([]\) | \(1050624\) | \(1.9318\) |
Rank
sage: E.rank()
The elliptic curves in class 150075n have rank \(1\).
Complex multiplication
The elliptic curves in class 150075n do not have complex multiplication.Modular form 150075.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.