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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 59150m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59150.n2 | 59150m1 | \([1, 1, 0, -2443940775, 50423834243125]\) | \(-21405018343206000779641/2177246093750000000\) | \(-164205485008239746093750000000\) | \([]\) | \(85349376\) | \(4.3457\) | \(\Gamma_0(N)\)-optimal |
| 59150.n3 | 59150m2 | \([1, 1, 0, 15050199850, -46245816147500]\) | \(4998853083179567995470359/2905108466204672000000\) | \(-219100057666451666432000000000000\) | \([]\) | \(256048128\) | \(4.8950\) | |
| 59150.n1 | 59150m3 | \([1, 1, 0, -213376009525, -40233643262081875]\) | \(-14245586655234650511684983641/1028175397808386133196800\) | \(-77543847870626538487336140800000000\) | \([]\) | \(768144384\) | \(5.4443\) |
Rank
sage: E.rank()
The elliptic curves in class 59150m have rank \(0\).
Complex multiplication
The elliptic curves in class 59150m do not have complex multiplication.Modular form 59150.2.a.m
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
