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SageMath
E = EllipticCurve("ic1")
E.isogeny_class()
Elliptic curves in class 73920.ic
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.ic1 | 73920ds4 | \([0, 1, 0, -65178785, -179406396225]\) | \(233632133015204766393938/29145526885986328125\) | \(3820162500000000000000000\) | \([2]\) | \(15728640\) | \(3.4465\) | |
| 73920.ic2 | 73920ds2 | \([0, 1, 0, -16280705, 22376420703]\) | \(7282213870869695463556/912102595400390625\) | \(59775555692160000000000\) | \([2, 2]\) | \(7864320\) | \(3.0999\) | |
| 73920.ic3 | 73920ds1 | \([0, 1, 0, -15755825, 24066219375]\) | \(26401417552259125806544/507547744790625\) | \(8315662250649600000\) | \([2]\) | \(3932160\) | \(2.7534\) | \(\Gamma_0(N)\)-optimal |
| 73920.ic4 | 73920ds3 | \([0, 1, 0, 24219295, 116020520703]\) | \(11986661998777424518222/51295853620928503125\) | \(-6723450125802340761600000\) | \([4]\) | \(15728640\) | \(3.4465\) |
Rank
sage: E.rank()
The elliptic curves in class 73920.ic have rank \(1\).
Complex multiplication
The elliptic curves in class 73920.ic do not have complex multiplication.Modular form 73920.2.a.ic
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
