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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 249090.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
249090.i1 | 249090i2 | \([1, 1, 0, -12403865172888, -16814493994372324032]\) | \(4486144075680775880097697589357030929/16270828779444633600\) | \(765475474529127478434201600\) | \([2]\) | \(4999680000\) | \(5.7397\) | |
249090.i2 | 249090i1 | \([1, 1, 0, -775241218968, -262726963100146368]\) | \(-1095248516670909925403006195052049/2085842527704615412039680\) | \(-98130299343130539825584752558080\) | \([2]\) | \(2499840000\) | \(5.3931\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 249090.i have rank \(0\).
Complex multiplication
The elliptic curves in class 249090.i do not have complex multiplication.Modular form 249090.2.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.