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SageMath
E = EllipticCurve("rc1")
E.isogeny_class()
Elliptic curves in class 235200rc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.rc3 | 235200rc1 | \([0, 1, 0, -15108, 592038]\) | \(3241792/567\) | \(66706983000000\) | \([2]\) | \(786432\) | \(1.3725\) | \(\Gamma_0(N)\)-optimal |
| 235200.rc2 | 235200rc2 | \([0, 1, 0, -70233, -6629337]\) | \(5088448/441\) | \(3320525376000000\) | \([2, 2]\) | \(1572864\) | \(1.7190\) | |
| 235200.rc4 | 235200rc3 | \([0, 1, 0, 76767, -30590337]\) | \(830584/7203\) | \(-433881982464000000\) | \([2]\) | \(3145728\) | \(2.0656\) | |
| 235200.rc1 | 235200rc4 | \([0, 1, 0, -1099233, -443954337]\) | \(2438569736/21\) | \(1264962048000000\) | \([2]\) | \(3145728\) | \(2.0656\) |
Rank
sage: E.rank()
The elliptic curves in class 235200rc have rank \(0\).
Complex multiplication
The elliptic curves in class 235200rc do not have complex multiplication.Modular form 235200.2.a.rc
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.
