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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 476850.do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 476850.do1 | 476850do1 | \([1, 0, 1, -1416251, -648428602]\) | \(832972004929/610368\) | \(230199995553000000\) | \([2]\) | \(8847360\) | \(2.2657\) | \(\Gamma_0(N)\)-optimal |
| 476850.do2 | 476850do2 | \([1, 0, 1, -1127251, -920666602]\) | \(-420021471169/727634952\) | \(-274427169698620125000\) | \([2]\) | \(17694720\) | \(2.6123\) |
Rank
sage: E.rank()
The elliptic curves in class 476850.do have rank \(0\).
Complex multiplication
The elliptic curves in class 476850.do do not have complex multiplication.Modular form 476850.2.a.do
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.
