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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 185130db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185130.bu4 | 185130db1 | \([1, -1, 0, -20395359, 35457415065]\) | \(726497538898787209/1038579300\) | \(1341291899216441700\) | \([2]\) | \(11059200\) | \(2.7496\) | \(\Gamma_0(N)\)-optimal |
| 185130.bu3 | 185130db2 | \([1, -1, 0, -20580489, 34781061123]\) | \(746461053445307689/27443694341250\) | \(35442652192750930421250\) | \([2]\) | \(22118400\) | \(3.0962\) | |
| 185130.bu2 | 185130db3 | \([1, -1, 0, -25965594, 14575825908]\) | \(1499114720492202169/796539777000000\) | \(1028705608029902913000000\) | \([2]\) | \(33177600\) | \(3.2989\) | |
| 185130.bu1 | 185130db4 | \([1, -1, 0, -239975874, -1419849476820]\) | \(1183430669265454849849/10449720703125000\) | \(13495479573082095703125000\) | \([2]\) | \(66355200\) | \(3.6455\) |
Rank
sage: E.rank()
The elliptic curves in class 185130db have rank \(0\).
Complex multiplication
The elliptic curves in class 185130db do not have complex multiplication.Modular form 185130.2.a.db
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
