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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 14784.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14784.ch1 | 14784bd3 | \([0, 1, 0, -14497, -676417]\) | \(1285429208617/614922\) | \(161198112768\) | \([2]\) | \(24576\) | \(1.1054\) | |
| 14784.ch2 | 14784bd4 | \([0, 1, 0, -8097, 273087]\) | \(223980311017/4278582\) | \(1121604599808\) | \([4]\) | \(24576\) | \(1.1054\) | |
| 14784.ch3 | 14784bd2 | \([0, 1, 0, -1057, -7105]\) | \(498677257/213444\) | \(55953063936\) | \([2, 2]\) | \(12288\) | \(0.75881\) | |
| 14784.ch4 | 14784bd1 | \([0, 1, 0, 223, -705]\) | \(4657463/3696\) | \(-968884224\) | \([2]\) | \(6144\) | \(0.41223\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14784.ch have rank \(1\).
Complex multiplication
The elliptic curves in class 14784.ch do not have complex multiplication.Modular form 14784.2.a.ch
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
