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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 9744.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9744.f1 | 9744l4 | \([0, -1, 0, -18704242992, 984602802313152]\) | \(176678690562294721133446471910833/3033870191363023488\) | \(12426732303822944206848\) | \([4]\) | \(11612160\) | \(4.2338\) | |
9744.f2 | 9744l3 | \([0, -1, 0, -1270909232, 12544321460160]\) | \(55425212630542527476751037873/15479334185118626660294016\) | \(63403352822245894800564289536\) | \([2]\) | \(11612160\) | \(4.2338\) | |
9744.f3 | 9744l2 | \([0, -1, 0, -1169051952, 15383694997440]\) | \(43138515777213631193352207793/5652352909513890349056\) | \(23152037517368894869733376\) | \([2, 2]\) | \(5806080\) | \(3.8872\) | |
9744.f4 | 9744l1 | \([0, -1, 0, -66736432, 283736078272]\) | \(-8025141932308829504241073/3845373573888057802752\) | \(-15750650158645484760072192\) | \([2]\) | \(2903040\) | \(3.5406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9744.f have rank \(0\).
Complex multiplication
The elliptic curves in class 9744.f do not have complex multiplication.Modular form 9744.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.