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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 37440.eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.eh1 | 37440ey6 | \([0, 0, 0, -5192652, -4554407536]\) | \(81025909800741361/11088090\) | \(2118966997155840\) | \([2]\) | \(786432\) | \(2.3531\) | |
| 37440.eh2 | 37440ey4 | \([0, 0, 0, -486732, 130599056]\) | \(66730743078481/60937500\) | \(11645337600000000\) | \([2]\) | \(393216\) | \(2.0065\) | |
| 37440.eh3 | 37440ey3 | \([0, 0, 0, -325452, -70742896]\) | \(19948814692561/231344100\) | \(44210545990041600\) | \([2, 2]\) | \(393216\) | \(2.0065\) | |
| 37440.eh4 | 37440ey5 | \([0, 0, 0, -66252, -180332656]\) | \(-168288035761/73415764890\) | \(-14029971155795312640\) | \([2]\) | \(786432\) | \(2.3531\) | |
| 37440.eh5 | 37440ey2 | \([0, 0, 0, -37452, 1026704]\) | \(30400540561/15210000\) | \(2906676264960000\) | \([2, 2]\) | \(196608\) | \(1.6600\) | |
| 37440.eh6 | 37440ey1 | \([0, 0, 0, 8628, 123536]\) | \(371694959/249600\) | \(-47699302809600\) | \([2]\) | \(98304\) | \(1.3134\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37440.eh have rank \(0\).
Complex multiplication
The elliptic curves in class 37440.eh do not have complex multiplication.Modular form 37440.2.a.eh
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
