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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 46200.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46200.c1 | 46200q2 | \([0, -1, 0, -229208, 2204412]\) | \(665863066004/384359283\) | \(768718566000000000\) | \([2]\) | \(645120\) | \(2.1215\) | |
46200.c2 | 46200q1 | \([0, -1, 0, -161708, 25019412]\) | \(935299949456/2750517\) | \(1375258500000000\) | \([2]\) | \(322560\) | \(1.7749\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46200.c have rank \(0\).
Complex multiplication
The elliptic curves in class 46200.c do not have complex multiplication.Modular form 46200.2.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.