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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 184910j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
184910.bb2 | 184910j1 | \([1, 0, 0, 16775, -3374375]\) | \(109902239/1100000\) | \(-5225114665100000\) | \([]\) | \(1408000\) | \(1.6971\) | \(\Gamma_0(N)\)-optimal |
184910.bb1 | 184910j2 | \([1, 0, 0, -9985175, -12145388665]\) | \(-23178622194826561/1610510\) | \(-7650090381172910\) | \([]\) | \(7040000\) | \(2.5019\) |
Rank
sage: E.rank()
The elliptic curves in class 184910j have rank \(1\).
Complex multiplication
The elliptic curves in class 184910j do not have complex multiplication.Modular form 184910.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.