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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 37905t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37905.s5 | 37905t1 | \([1, 0, 1, -72208, -8535319]\) | \(-885012508801/155859375\) | \(-7332541608984375\) | \([2]\) | \(253440\) | \(1.7700\) | \(\Gamma_0(N)\)-optimal |
| 37905.s4 | 37905t2 | \([1, 0, 1, -1200333, -506264069]\) | \(4065433152958801/99500625\) | \(4681094563175625\) | \([2, 2]\) | \(506880\) | \(2.1166\) | |
| 37905.s3 | 37905t3 | \([1, 0, 1, -1245458, -466156969]\) | \(4541390686576801/633623960025\) | \(29809397422084907025\) | \([2, 2]\) | \(1013760\) | \(2.4631\) | |
| 37905.s1 | 37905t4 | \([1, 0, 1, -19205208, -32396498669]\) | \(16651720753282540801/9975\) | \(469282662975\) | \([2]\) | \(1013760\) | \(2.4631\) | |
| 37905.s6 | 37905t5 | \([1, 0, 1, 2012567, -2495254939]\) | \(19162556947522799/68270261146605\) | \(-3211834581742102384005\) | \([2]\) | \(2027520\) | \(2.8097\) | |
| 37905.s2 | 37905t6 | \([1, 0, 1, -5225483, 4129975901]\) | \(335414091635204401/37448756505405\) | \(1761809742151259486805\) | \([2]\) | \(2027520\) | \(2.8097\) |
Rank
sage: E.rank()
The elliptic curves in class 37905t have rank \(0\).
Complex multiplication
The elliptic curves in class 37905t do not have complex multiplication.Modular form 37905.2.a.t
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
