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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 250470q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250470.q2 | 250470q1 | \([1, -1, 0, -601695, 2364887421]\) | \(-14014952531/1397250000\) | \(-2401794317801067750000\) | \([2]\) | \(11151360\) | \(2.7821\) | \(\Gamma_0(N)\)-optimal |
250470.q1 | 250470q2 | \([1, -1, 0, -30549195, 64517928921]\) | \(1834261866512531/15618460500\) | \(26847256884380335309500\) | \([2]\) | \(22302720\) | \(3.1287\) |
Rank
sage: E.rank()
The elliptic curves in class 250470q have rank \(1\).
Complex multiplication
The elliptic curves in class 250470q do not have complex multiplication.Modular form 250470.2.a.q
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.