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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 393008j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
393008.j2 | 393008j1 | \([0, 1, 0, -18432, 1007092]\) | \(-95443993/5887\) | \(-42717919670272\) | \([2]\) | \(983040\) | \(1.3699\) | \(\Gamma_0(N)\)-optimal |
393008.j1 | 393008j2 | \([0, 1, 0, -299152, 62877780]\) | \(408023180713/1421\) | \(10311221989376\) | \([2]\) | \(1966080\) | \(1.7165\) |
Rank
sage: E.rank()
The elliptic curves in class 393008j have rank \(1\).
Complex multiplication
The elliptic curves in class 393008j do not have complex multiplication.Modular form 393008.2.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.