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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 33150h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33150.c1 | 33150h1 | \([1, 1, 0, -16436250, 25641076500]\) | \(31427652507069423952801/654426190080\) | \(10225409220000000\) | \([2]\) | \(1167360\) | \(2.6013\) | \(\Gamma_0(N)\)-optimal |
33150.c2 | 33150h2 | \([1, 1, 0, -16418250, 25700062500]\) | \(-31324512477868037557921/143427974919699600\) | \(-2241062108120306250000\) | \([2]\) | \(2334720\) | \(2.9479\) |
Rank
sage: E.rank()
The elliptic curves in class 33150h have rank \(1\).
Complex multiplication
The elliptic curves in class 33150h do not have complex multiplication.Modular form 33150.2.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.