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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 203280.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203280.h1 | 203280el1 | \([0, -1, 0, -718296, 231592176]\) | \(4243659659/61740\) | \(596294412051824640\) | \([2]\) | \(3041280\) | \(2.2145\) | \(\Gamma_0(N)\)-optimal |
203280.h2 | 203280el2 | \([0, -1, 0, -79416, 628208880]\) | \(-5735339/17647350\) | \(-170440819444813209600\) | \([2]\) | \(6082560\) | \(2.5610\) |
Rank
sage: E.rank()
The elliptic curves in class 203280.h have rank \(0\).
Complex multiplication
The elliptic curves in class 203280.h do not have complex multiplication.Modular form 203280.2.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 LMFDB 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 LMFDB labels.