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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 187850.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187850.e1 | 187850x2 | \([1, 0, 1, -1278304526, 17590827584448]\) | \(3009261308803109129809313/85820312500000000\) | \(6588049926757812500000000\) | \([2]\) | \(70778880\) | \(3.8636\) | |
| 187850.e2 | 187850x1 | \([1, 0, 1, -83136526, 251330240448]\) | \(827813553991775477153/123566310400000000\) | \(9485645046800000000000000\) | \([2]\) | \(35389440\) | \(3.5170\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 187850.e have rank \(0\).
Complex multiplication
The elliptic curves in class 187850.e do not have complex multiplication.Modular form 187850.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
