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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 243360.ep
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
243360.ep1 | 243360ep2 | \([0, 0, 0, -2008227, 1095024346]\) | \(497169541448/190125\) | \(342528592670784000\) | \([2]\) | \(5160960\) | \(2.3305\) | |
243360.ep2 | 243360ep1 | \([0, 0, 0, -106977, 22339096]\) | \(-601211584/609375\) | \(-137231006679000000\) | \([2]\) | \(2580480\) | \(1.9839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 243360.ep have rank \(1\).
Complex multiplication
The elliptic curves in class 243360.ep do not have complex multiplication.Modular form 243360.2.a.ep
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.