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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 9075h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9075.o2 | 9075h1 | \([1, 1, 0, -970, -79625]\) | \(-343/9\) | \(-2652691152375\) | \([2]\) | \(16896\) | \(1.0645\) | \(\Gamma_0(N)\)-optimal |
9075.o1 | 9075h2 | \([1, 1, 0, -34245, -2442150]\) | \(15069223/81\) | \(23874220371375\) | \([2]\) | \(33792\) | \(1.4110\) |
Rank
sage: E.rank()
The elliptic curves in class 9075h have rank \(0\).
Complex multiplication
The elliptic curves in class 9075h do not have complex multiplication.Modular form 9075.2.a.h
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.