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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 111600j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111600.k2 | 111600j1 | \([0, 0, 0, -3075, -352750]\) | \(-7443468/120125\) | \(-51894000000000\) | \([2]\) | \(258048\) | \(1.3130\) | \(\Gamma_0(N)\)-optimal |
111600.k1 | 111600j2 | \([0, 0, 0, -96075, -11419750]\) | \(113511836214/484375\) | \(418500000000000\) | \([2]\) | \(516096\) | \(1.6595\) |
Rank
sage: E.rank()
The elliptic curves in class 111600j have rank \(2\).
Complex multiplication
The elliptic curves in class 111600j do not have complex multiplication.Modular form 111600.2.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.