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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 10350.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10350.d1 | 10350t2 | \([1, -1, 0, -169542, 11953116]\) | \(47316161414809/22001657400\) | \(250612628821875000\) | \([2]\) | \(129024\) | \(2.0331\) | |
10350.d2 | 10350t1 | \([1, -1, 0, 37458, 1396116]\) | \(510273943271/370215360\) | \(-4216984335000000\) | \([2]\) | \(64512\) | \(1.6865\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10350.d have rank \(1\).
Complex multiplication
The elliptic curves in class 10350.d do not have complex multiplication.Modular form 10350.2.a.d
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.