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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 5184.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5184.c1 | 5184m2 | \([0, 0, 0, -3564, -89424]\) | \(-35937/4\) | \(-557256278016\) | \([]\) | \(6912\) | \(0.99122\) | |
| 5184.c2 | 5184m1 | \([0, 0, 0, 276, 176]\) | \(109503/64\) | \(-1358954496\) | \([]\) | \(2304\) | \(0.44191\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5184.c have rank \(1\).
Complex multiplication
The elliptic curves in class 5184.c do not have complex multiplication.Modular form 5184.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
