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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 3024.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3024.c1 | 3024r1 | \([0, 0, 0, -2259, -41326]\) | \(-11527859979/28\) | \(-3096576\) | \([]\) | \(1728\) | \(0.48579\) | \(\Gamma_0(N)\)-optimal |
| 3024.c2 | 3024r2 | \([0, 0, 0, -1539, -68094]\) | \(-5000211/21952\) | \(-1769804660736\) | \([]\) | \(5184\) | \(1.0351\) | |
| 3024.c3 | 3024r3 | \([0, 0, 0, 13581, 1646514]\) | \(381790581/1835008\) | \(-1331471000272896\) | \([]\) | \(15552\) | \(1.5844\) |
Rank
sage: E.rank()
The elliptic curves in class 3024.c have rank \(0\).
Complex multiplication
The elliptic curves in class 3024.c do not have complex multiplication.Modular form 3024.2.a.c
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.
