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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 309738.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
309738.p1 | 309738p2 | \([1, 1, 0, -2661299, 1667944173]\) | \(44308125149913793/61165323648\) | \(2877576537670293888\) | \([2]\) | \(13208832\) | \(2.4463\) | |
309738.p2 | 309738p1 | \([1, 1, 0, -119859, 40914285]\) | \(-4047806261953/13066420224\) | \(-614721250954297344\) | \([2]\) | \(6604416\) | \(2.0997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 309738.p have rank \(0\).
Complex multiplication
The elliptic curves in class 309738.p do not have complex multiplication.Modular form 309738.2.a.p
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.