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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 2450.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2450.x1 | 2450bf2 | \([1, 1, 1, -55763, 7098531]\) | \(-417267265/235298\) | \(-10813505625781250\) | \([]\) | \(17280\) | \(1.7798\) | |
2450.x2 | 2450bf1 | \([1, 1, 1, 5487, -128969]\) | \(397535/392\) | \(-18015003125000\) | \([]\) | \(5760\) | \(1.2305\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2450.x have rank \(0\).
Complex multiplication
The elliptic curves in class 2450.x do not have complex multiplication.Modular form 2450.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.