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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 212160.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212160.c1 | 212160hb2 | \([0, -1, 0, -98961, -11509839]\) | \(6541847063933776/272710546875\) | \(4468089600000000\) | \([2]\) | \(1474560\) | \(1.7680\) | |
212160.c2 | 212160hb1 | \([0, -1, 0, -16341, 569205]\) | \(471287826743296/138654433125\) | \(141982139520000\) | \([2]\) | \(737280\) | \(1.4214\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 212160.c have rank \(1\).
Complex multiplication
The elliptic curves in class 212160.c do not have complex multiplication.Modular form 212160.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.