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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 103428.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103428.w1 | 103428bb1 | \([0, 0, 0, -421824, -66461447]\) | \(67108864/23409\) | \(2895479825994304848\) | \([2]\) | \(1437696\) | \(2.2440\) | \(\Gamma_0(N)\)-optimal |
| 103428.w2 | 103428bb2 | \([0, 0, 0, 1258881, -464116250]\) | \(111485936/111537\) | \(-220737756146389357824\) | \([2]\) | \(2875392\) | \(2.5905\) |
Rank
sage: E.rank()
The elliptic curves in class 103428.w have rank \(0\).
Complex multiplication
The elliptic curves in class 103428.w do not have complex multiplication.Modular form 103428.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
