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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 147175p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
147175.o2 | 147175p1 | \([1, 1, 0, -200175, 36179000]\) | \(-95443993/5887\) | \(-54714451417609375\) | \([2]\) | \(1290240\) | \(1.9662\) | \(\Gamma_0(N)\)-optimal |
147175.o1 | 147175p2 | \([1, 1, 0, -3248800, 2252529375]\) | \(408023180713/1421\) | \(13206936549078125\) | \([2]\) | \(2580480\) | \(2.3127\) |
Rank
sage: E.rank()
The elliptic curves in class 147175p have rank \(1\).
Complex multiplication
The elliptic curves in class 147175p do not have complex multiplication.Modular form 147175.2.a.p
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.