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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 65520.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
65520.i1 | 65520bt2 | \([0, 0, 0, -852843, 303144858]\) | \(620307836233921107/2548000000\) | \(281788416000000\) | \([2]\) | \(589824\) | \(1.9826\) | |
65520.i2 | 65520bt1 | \([0, 0, 0, -54123, 4583322]\) | \(158542456758867/9691136000\) | \(1071762112512000\) | \([2]\) | \(294912\) | \(1.6360\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 65520.i have rank \(0\).
Complex multiplication
The elliptic curves in class 65520.i do not have complex multiplication.Modular form 65520.2.a.i
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.