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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 329476j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
329476.j1 | 329476j1 | \([0, 1, 0, -74524, -8208572]\) | \(-768208/41\) | \(-2442997611563264\) | \([]\) | \(1935360\) | \(1.7116\) | \(\Gamma_0(N)\)-optimal |
329476.j2 | 329476j2 | \([0, 1, 0, 396156, -17057356]\) | \(115393712/68921\) | \(-4106678985037846784\) | \([]\) | \(5806080\) | \(2.2609\) |
Rank
sage: E.rank()
The elliptic curves in class 329476j have rank \(1\).
Complex multiplication
The elliptic curves in class 329476j do not have complex multiplication.Modular form 329476.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.