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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 479808.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479808.i1 | 479808i2 | \([0, 0, 0, -28812, -1289680]\) | \(941192/289\) | \(812201049096192\) | \([2]\) | \(2654208\) | \(1.5656\) | |
479808.i2 | 479808i1 | \([0, 0, 0, -11172, 439040]\) | \(438976/17\) | \(5972066537472\) | \([2]\) | \(1327104\) | \(1.2190\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 479808.i have rank \(0\).
Complex multiplication
The elliptic curves in class 479808.i do not have complex multiplication.Modular form 479808.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.