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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 28314.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28314.c1 | 28314x1 | \([1, -1, 0, -7101, 1539621]\) | \(-30664297/773344\) | \(-998749005018336\) | \([]\) | \(172800\) | \(1.5588\) | \(\Gamma_0(N)\)-optimal |
28314.c2 | 28314x2 | \([1, -1, 0, 63684, -40719024]\) | \(22117051943/566984704\) | \(-732242584128946176\) | \([]\) | \(518400\) | \(2.1081\) |
Rank
sage: E.rank()
The elliptic curves in class 28314.c have rank \(1\).
Complex multiplication
The elliptic curves in class 28314.c do not have complex multiplication.Modular form 28314.2.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.