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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 37030q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37030.o3 | 37030q1 | \([1, 0, 0, -79890, -8445500]\) | \(380920459249/12622400\) | \(1868568205313600\) | \([2]\) | \(304128\) | \(1.7034\) | \(\Gamma_0(N)\)-optimal |
| 37030.o4 | 37030q2 | \([1, 0, 0, 25910, -29161140]\) | \(12994449551/2489452840\) | \(-368528364292974760\) | \([2]\) | \(608256\) | \(2.0499\) | |
| 37030.o1 | 37030q3 | \([1, 0, 0, -894550, 322765632]\) | \(534774372149809/5323062500\) | \(788004289390062500\) | \([2]\) | \(912384\) | \(2.2527\) | |
| 37030.o2 | 37030q4 | \([1, 0, 0, -233300, 789475882]\) | \(-9486391169809/1813439640250\) | \(-268454149292248932250\) | \([2]\) | \(1824768\) | \(2.5992\) |
Rank
sage: E.rank()
The elliptic curves in class 37030q have rank \(0\).
Complex multiplication
The elliptic curves in class 37030q do not have complex multiplication.Modular form 37030.2.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 Cremona 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 Cremona labels.
