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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 23805t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23805.s7 | 23805t1 | \([1, -1, 0, -99, 61240]\) | \(-1/15\) | \(-1618772446215\) | \([2]\) | \(25344\) | \(1.0216\) | \(\Gamma_0(N)\)-optimal |
| 23805.s6 | 23805t2 | \([1, -1, 0, -23904, 1408603]\) | \(13997521/225\) | \(24281586693225\) | \([2, 2]\) | \(50688\) | \(1.3682\) | |
| 23805.s5 | 23805t3 | \([1, -1, 0, -47709, -1843160]\) | \(111284641/50625\) | \(5463357005975625\) | \([2, 2]\) | \(101376\) | \(1.7148\) | |
| 23805.s4 | 23805t4 | \([1, -1, 0, -380979, 90605938]\) | \(56667352321/15\) | \(1618772446215\) | \([2]\) | \(101376\) | \(1.7148\) | |
| 23805.s8 | 23805t5 | \([1, -1, 0, 166536, -13969427]\) | \(4733169839/3515625\) | \(-379399792081640625\) | \([2]\) | \(202752\) | \(2.0613\) | |
| 23805.s2 | 23805t6 | \([1, -1, 0, -642834, -198115385]\) | \(272223782641/164025\) | \(17701276699361025\) | \([2, 2]\) | \(202752\) | \(2.0613\) | |
| 23805.s3 | 23805t7 | \([1, -1, 0, -523809, -273839090]\) | \(-147281603041/215233605\) | \(-23227615284901537005\) | \([2]\) | \(405504\) | \(2.4079\) | |
| 23805.s1 | 23805t8 | \([1, -1, 0, -10283859, -12690955580]\) | \(1114544804970241/405\) | \(43706856047805\) | \([2]\) | \(405504\) | \(2.4079\) |
Rank
sage: E.rank()
The elliptic curves in class 23805t have rank \(0\).
Complex multiplication
The elliptic curves in class 23805t do not have complex multiplication.Modular form 23805.2.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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
