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SageMath
E = EllipticCurve("ge1")
E.isogeny_class()
Elliptic curves in class 84150.ge
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.ge1 | 84150et1 | \([1, -1, 1, -44105, 3573897]\) | \(832972004929/610368\) | \(6952473000000\) | \([2]\) | \(245760\) | \(1.3984\) | \(\Gamma_0(N)\)-optimal |
| 84150.ge2 | 84150et2 | \([1, -1, 1, -35105, 5067897]\) | \(-420021471169/727634952\) | \(-8288216875125000\) | \([2]\) | \(491520\) | \(1.7450\) |
Rank
sage: E.rank()
The elliptic curves in class 84150.ge have rank \(1\).
Complex multiplication
The elliptic curves in class 84150.ge do not have complex multiplication.Modular form 84150.2.a.ge
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.
