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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 4400.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4400.w1 | 4400l1 | \([0, 1, 0, -35408, -2600812]\) | \(-76711450249/851840\) | \(-54517760000000\) | \([]\) | \(16128\) | \(1.4507\) | \(\Gamma_0(N)\)-optimal |
4400.w2 | 4400l2 | \([0, 1, 0, 118592, -13380812]\) | \(2882081488391/2883584000\) | \(-184549376000000000\) | \([]\) | \(48384\) | \(2.0000\) |
Rank
sage: E.rank()
The elliptic curves in class 4400.w have rank \(0\).
Complex multiplication
The elliptic curves in class 4400.w do not have complex multiplication.Modular form 4400.2.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.