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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 7800d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7800.t4 | 7800d1 | \([0, 1, 0, 4217, 8438]\) | \(33165879296/19278675\) | \(-4819668750000\) | \([2]\) | \(9216\) | \(1.1231\) | \(\Gamma_0(N)\)-optimal |
| 7800.t3 | 7800d2 | \([0, 1, 0, -16908, 50688]\) | \(133649126224/77000625\) | \(308002500000000\) | \([2, 2]\) | \(18432\) | \(1.4697\) | |
| 7800.t2 | 7800d3 | \([0, 1, 0, -179408, -29199312]\) | \(39914580075556/172718325\) | \(2763493200000000\) | \([2]\) | \(36864\) | \(1.8162\) | |
| 7800.t1 | 7800d4 | \([0, 1, 0, -192408, 32342688]\) | \(49235161015876/137109375\) | \(2193750000000000\) | \([2]\) | \(36864\) | \(1.8162\) |
Rank
sage: E.rank()
The elliptic curves in class 7800d have rank \(0\).
Complex multiplication
The elliptic curves in class 7800d do not have complex multiplication.Modular form 7800.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
