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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 203390.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203390.j1 | 203390q2 | \([1, 0, 1, -10983099, 14008998396]\) | \(-23178622194826561/1610510\) | \(-10180618404044990\) | \([]\) | \(8064000\) | \(2.5257\) | |
203390.j2 | 203390q1 | \([1, 0, 1, 18451, 3895816]\) | \(109902239/1100000\) | \(-6953499353900000\) | \([]\) | \(1612800\) | \(1.7210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 203390.j have rank \(1\).
Complex multiplication
The elliptic curves in class 203390.j do not have complex multiplication.Modular form 203390.2.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 LMFDB 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 LMFDB labels.