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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1479.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1479.c1 | 1479f1 | \([0, 1, 1, -6070, 181852]\) | \(-24737814642405376/290166236091\) | \(-290166236091\) | \([5]\) | \(2400\) | \(1.0122\) | \(\Gamma_0(N)\)-optimal |
1479.c2 | 1479f2 | \([0, 1, 1, 39320, -6363488]\) | \(6722846486548803584/21456068898310251\) | \(-21456068898310251\) | \([]\) | \(12000\) | \(1.8169\) |
Rank
sage: E.rank()
The elliptic curves in class 1479.c have rank \(1\).
Complex multiplication
The elliptic curves in class 1479.c do not have complex multiplication.Modular form 1479.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.