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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 187590.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187590.g1 | 187590ct3 | \([1, 1, 0, -57629848, 168367163008]\) | \(4385367890843575421521/24975000000\) | \(120549554775000000\) | \([2]\) | \(15925248\) | \(2.8893\) | |
| 187590.g2 | 187590ct6 | \([1, 1, 0, -51228128, -140535029448]\) | \(3080272010107543650001/15465841417699560\) | \(74650662547524995504040\) | \([2]\) | \(31850496\) | \(3.2359\) | |
| 187590.g3 | 187590ct4 | \([1, 1, 0, -4955928, 474872832]\) | \(2788936974993502801/1593609593601600\) | \(7692049128882545294400\) | \([2, 2]\) | \(15925248\) | \(2.8893\) | |
| 187590.g4 | 187590ct2 | \([1, 1, 0, -3603928, 2626445632]\) | \(1072487167529950801/2554882560000\) | \(12331930134551040000\) | \([2, 2]\) | \(7962624\) | \(2.5427\) | |
| 187590.g5 | 187590ct1 | \([1, 1, 0, -142808, 71446848]\) | \(-66730743078481/419010969600\) | \(-2022485919164006400\) | \([2]\) | \(3981312\) | \(2.1961\) | \(\Gamma_0(N)\)-optimal |
| 187590.g6 | 187590ct5 | \([1, 1, 0, 19684272, 3811155912]\) | \(174751791402194852399/102423900876336360\) | \(-494380606565008229475240\) | \([2]\) | \(31850496\) | \(3.2359\) |
Rank
sage: E.rank()
The elliptic curves in class 187590.g have rank \(1\).
Complex multiplication
The elliptic curves in class 187590.g do not have complex multiplication.Modular form 187590.2.a.g
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
