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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 33813i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33813.p2 | 33813i1 | \([1, -1, 0, -1905720, -1010469277]\) | \(43499078731809/82055753\) | \(1443876645515769153\) | \([2]\) | \(1105920\) | \(2.3745\) | \(\Gamma_0(N)\)-optimal |
33813.p1 | 33813i2 | \([1, -1, 0, -30477705, -64754567812]\) | \(177930109857804849/634933\) | \(11172463802352333\) | \([2]\) | \(2211840\) | \(2.7211\) |
Rank
sage: E.rank()
The elliptic curves in class 33813i have rank \(0\).
Complex multiplication
The elliptic curves in class 33813i do not have complex multiplication.Modular form 33813.2.a.i
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.