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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 334620.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
334620.j1 | 334620j1 | \([0, 0, 0, -2709408, -1718396732]\) | \(-2441851961344/3020875\) | \(-2721199375106784000\) | \([]\) | \(6967296\) | \(2.4468\) | \(\Gamma_0(N)\)-optimal |
334620.j2 | 334620j2 | \([0, 0, 0, 3617952, -7965715628]\) | \(5814126903296/33794921875\) | \(-30442411648291500000000\) | \([]\) | \(20901888\) | \(2.9961\) |
Rank
sage: E.rank()
The elliptic curves in class 334620.j have rank \(1\).
Complex multiplication
The elliptic curves in class 334620.j do not have complex multiplication.Modular form 334620.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.