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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 3850e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3850.l1 | 3850e1 | \([1, 1, 0, -27825, 6327125]\) | \(-243979633825/1636214272\) | \(-15978655000000000\) | \([]\) | \(25920\) | \(1.7925\) | \(\Gamma_0(N)\)-optimal |
3850.l2 | 3850e2 | \([1, 1, 0, 247175, -158947875]\) | \(171015136702175/1218033273688\) | \(-11894856188359375000\) | \([]\) | \(77760\) | \(2.3418\) |
Rank
sage: E.rank()
The elliptic curves in class 3850e have rank \(0\).
Complex multiplication
The elliptic curves in class 3850e do not have complex multiplication.Modular form 3850.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.