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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 35322.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35322.d1 | 35322h2 | \([1, 1, 0, -534609420, 4192138756062]\) | \(1164800512406592125/150691848242418\) | \(2186108639826256329090211242\) | \([2]\) | \(24009216\) | \(3.9746\) | |
35322.d2 | 35322h1 | \([1, 1, 0, 50970470, 342887907136]\) | \(1009479798755875/4084868810988\) | \(-59259788133277350970048572\) | \([2]\) | \(12004608\) | \(3.6280\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35322.d have rank \(0\).
Complex multiplication
The elliptic curves in class 35322.d do not have complex multiplication.Modular form 35322.2.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.