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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 59850bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59850.cu3 | 59850bs1 | \([1, -1, 0, -2964942, 1965509716]\) | \(253060782505556761/41184460800\) | \(469116748800000000\) | \([2]\) | \(1179648\) | \(2.3998\) | \(\Gamma_0(N)\)-optimal |
| 59850.cu2 | 59850bs2 | \([1, -1, 0, -3252942, 1560869716]\) | \(334199035754662681/101099003040000\) | \(1151580831502500000000\) | \([2, 2]\) | \(2359296\) | \(2.7464\) | |
| 59850.cu4 | 59850bs3 | \([1, -1, 0, 8897058, 10466819716]\) | \(6837784281928633319/8113766016106800\) | \(-92420866027216518750000\) | \([2]\) | \(4718592\) | \(3.0930\) | |
| 59850.cu1 | 59850bs4 | \([1, -1, 0, -20010942, -33245496284]\) | \(77799851782095807001/3092322318750000\) | \(35223483912011718750000\) | \([2]\) | \(4718592\) | \(3.0930\) |
Rank
sage: E.rank()
The elliptic curves in class 59850bs have rank \(1\).
Complex multiplication
The elliptic curves in class 59850bs do not have complex multiplication.Modular form 59850.2.a.bs
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.
