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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 360789e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
360789.e2 | 360789e1 | \([1, 0, 0, -9005742131, -330371723572032]\) | \(-135798272907989852399888089/681332888130948168687\) | \(-405272691224572072577269549527\) | \([2]\) | \(955100160\) | \(4.5285\) | \(\Gamma_0(N)\)-optimal |
360789.e1 | 360789e2 | \([1, 0, 0, -144264936916, -21090629235147757]\) | \(558236327843639730114488861929/13948140496113173493\) | \(8296679251672625448955430253\) | \([2]\) | \(1910200320\) | \(4.8750\) |
Rank
sage: E.rank()
The elliptic curves in class 360789e have rank \(0\).
Complex multiplication
The elliptic curves in class 360789e do not have complex multiplication.Modular form 360789.2.a.e
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 Cremona 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 Cremona labels.