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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 18130.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18130.q1 | 18130m3 | \([1, 1, 1, -258476, 50472253]\) | \(16232905099479601/4052240\) | \(476741983760\) | \([2]\) | \(103680\) | \(1.6165\) | |
| 18130.q2 | 18130m4 | \([1, 1, 1, -257496, 50875229]\) | \(-16048965315233521/256572640900\) | \(-30185514629244100\) | \([2]\) | \(207360\) | \(1.9630\) | |
| 18130.q3 | 18130m1 | \([1, 1, 1, -3676, 45373]\) | \(46694890801/18944000\) | \(2228742656000\) | \([2]\) | \(34560\) | \(1.0672\) | \(\Gamma_0(N)\)-optimal |
| 18130.q4 | 18130m2 | \([1, 1, 1, 12004, 346429]\) | \(1625964918479/1369000000\) | \(-161061481000000\) | \([2]\) | \(69120\) | \(1.4137\) |
Rank
sage: E.rank()
The elliptic curves in class 18130.q have rank \(0\).
Complex multiplication
The elliptic curves in class 18130.q do not have complex multiplication.Modular form 18130.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
