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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 13520.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13520.e1 | 13520bg2 | \([0, 1, 0, -1591360, -765036492]\) | \(10260751717/125000\) | \(5429503678976000000\) | \([2]\) | \(269568\) | \(2.4055\) | |
13520.e2 | 13520bg1 | \([0, 1, 0, -185280, 11682100]\) | \(16194277/8000\) | \(347488235454464000\) | \([2]\) | \(134784\) | \(2.0589\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13520.e have rank \(0\).
Complex multiplication
The elliptic curves in class 13520.e do not have complex multiplication.Modular form 13520.2.a.e
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.