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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 62400dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.hq3 | 62400dd1 | \([0, 1, 0, -11133, 447363]\) | \(9538484224/26325\) | \(421200000000\) | \([2]\) | \(147456\) | \(1.1035\) | \(\Gamma_0(N)\)-optimal |
| 62400.hq2 | 62400dd2 | \([0, 1, 0, -15633, 46863]\) | \(1650587344/950625\) | \(243360000000000\) | \([2, 2]\) | \(294912\) | \(1.4500\) | |
| 62400.hq4 | 62400dd3 | \([0, 1, 0, 62367, 436863]\) | \(26198797244/15234375\) | \(-15600000000000000\) | \([2]\) | \(589824\) | \(1.7966\) | |
| 62400.hq1 | 62400dd4 | \([0, 1, 0, -165633, -25903137]\) | \(490757540836/2142075\) | \(2193484800000000\) | \([2]\) | \(589824\) | \(1.7966\) |
Rank
sage: E.rank()
The elliptic curves in class 62400dd have rank \(1\).
Complex multiplication
The elliptic curves in class 62400dd do not have complex multiplication.Modular form 62400.2.a.dd
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.
