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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 301180e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301180.e1 | 301180e1 | \([0, 0, 0, -366892, 77651049]\) | \(133047926784/13542925\) | \(555959045241701200\) | \([2]\) | \(3677184\) | \(2.1408\) | \(\Gamma_0(N)\)-optimal |
| 301180.e2 | 301180e2 | \([0, 0, 0, 461353, 377972686]\) | \(16533829296/103530625\) | \(-68001602227910560000\) | \([2]\) | \(7354368\) | \(2.4873\) |
Rank
sage: E.rank()
The elliptic curves in class 301180e have rank \(1\).
Complex multiplication
The elliptic curves in class 301180e do not have complex multiplication.Modular form 301180.2.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.
