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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 433200l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
433200.l2 | 433200l1 | \([0, -1, 0, 8867, -315488]\) | \(44957696/50625\) | \(-86809218750000\) | \([2]\) | \(1105920\) | \(1.3610\) | \(\Gamma_0(N)\)-optimal* |
433200.l1 | 433200l2 | \([0, -1, 0, -50508, -2927988]\) | \(519388144/164025\) | \(4500189900000000\) | \([2]\) | \(2211840\) | \(1.7076\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 433200l have rank \(2\).
Complex multiplication
The elliptic curves in class 433200l do not have complex multiplication.Modular form 433200.2.a.l
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.