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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 361998e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361998.e2 | 361998e1 | \([1, -1, 0, -32733, -3188795]\) | \(-1102302937/616896\) | \(-2170698951185856\) | \([2]\) | \(1658880\) | \(1.6461\) | \(\Gamma_0(N)\)-optimal |
| 361998.e1 | 361998e2 | \([1, -1, 0, -580293, -169975571]\) | \(6141556990297/1019592\) | \(3587682988765512\) | \([2]\) | \(3317760\) | \(1.9927\) |
Rank
sage: E.rank()
The elliptic curves in class 361998e have rank \(0\).
Complex multiplication
The elliptic curves in class 361998e do not have complex multiplication.Modular form 361998.2.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 Cremona 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 Cremona labels.
