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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 2450.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2450.w1 | 2450s2 | \([1, 1, 1, -39838, -3338469]\) | \(-77626969/8000\) | \(-720600125000000\) | \([]\) | \(12096\) | \(1.5904\) | |
2450.w2 | 2450s1 | \([1, 1, 1, 3037, 5781]\) | \(34391/20\) | \(-1801500312500\) | \([]\) | \(4032\) | \(1.0411\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2450.w have rank \(0\).
Complex multiplication
The elliptic curves in class 2450.w do not have complex multiplication.Modular form 2450.2.a.w
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.