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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 190400.el
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190400.el1 | 190400eo2 | \([0, -1, 0, -44833, 453537]\) | \(2433138625/1387778\) | \(5684338688000000\) | \([2]\) | \(884736\) | \(1.7128\) | |
190400.el2 | 190400eo1 | \([0, -1, 0, -28833, -1866463]\) | \(647214625/3332\) | \(13647872000000\) | \([2]\) | \(442368\) | \(1.3663\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190400.el have rank \(1\).
Complex multiplication
The elliptic curves in class 190400.el do not have complex multiplication.Modular form 190400.2.a.el
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.