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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 388815w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388815.w3 | 388815w1 | \([1, 1, 1, -7258420, 7501930820]\) | \(2428257525121/8150625\) | \(141953520756872750625\) | \([4]\) | \(12976128\) | \(2.7311\) | \(\Gamma_0(N)\)-optimal |
| 388815.w2 | 388815w2 | \([1, 1, 1, -10498545, 136478670]\) | \(7347774183121/4251692025\) | \(74048634567615101636025\) | \([2, 2]\) | \(25952256\) | \(3.0777\) | |
| 388815.w4 | 388815w3 | \([1, 1, 1, 41991480, 1144287150]\) | \(470166844956479/272118787605\) | \(-4739295448462101356808405\) | \([2]\) | \(51904512\) | \(3.4243\) | |
| 388815.w1 | 388815w4 | \([1, 1, 1, -114830570, -472195464910]\) | \(9614816895690721/34652610405\) | \(603519368196425691719205\) | \([2]\) | \(51904512\) | \(3.4243\) |
Rank
sage: E.rank()
The elliptic curves in class 388815w have rank \(2\).
Complex multiplication
The elliptic curves in class 388815w do not have complex multiplication.Modular form 388815.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
