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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 5635j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5635.c1 | 5635j1 | \([1, -1, 1, -7972, 275846]\) | \(476196576129/197225\) | \(23203324025\) | \([2]\) | \(6912\) | \(0.95094\) | \(\Gamma_0(N)\)-optimal |
5635.c2 | 5635j2 | \([1, -1, 1, -6747, 362576]\) | \(-288673724529/311181605\) | \(-36610204646645\) | \([2]\) | \(13824\) | \(1.2975\) |
Rank
sage: E.rank()
The elliptic curves in class 5635j have rank \(0\).
Complex multiplication
The elliptic curves in class 5635j do not have complex multiplication.Modular form 5635.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.