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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 270480.et
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270480.et1 | 270480et2 | \([0, -1, 0, -41960, 3037392]\) | \(33909572018/3234375\) | \(779306976000000\) | \([2]\) | \(1548288\) | \(1.5953\) | |
270480.et2 | 270480et1 | \([0, -1, 0, 3120, 224400]\) | \(27871484/198375\) | \(-23898747264000\) | \([2]\) | \(774144\) | \(1.2487\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270480.et have rank \(1\).
Complex multiplication
The elliptic curves in class 270480.et do not have complex multiplication.Modular form 270480.2.a.et
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.