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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 3024.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3024.f1 | 3024s3 | \([0, 0, 0, -61344, 5847984]\) | \(35184082944/7\) | \(5079158784\) | \([]\) | \(7776\) | \(1.2518\) | |
| 3024.f2 | 3024s2 | \([0, 0, 0, -864, 5616]\) | \(884736/343\) | \(27653197824\) | \([]\) | \(2592\) | \(0.70248\) | |
| 3024.f3 | 3024s1 | \([0, 0, 0, -384, -2896]\) | \(56623104/7\) | \(774144\) | \([]\) | \(864\) | \(0.15317\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3024.f have rank \(0\).
Complex multiplication
The elliptic curves in class 3024.f do not have complex multiplication.Modular form 3024.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
