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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 11830.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11830.t1 | 11830t3 | \([1, -1, 1, -18427792, -30442429741]\) | \(143378317900125424089/4976562500000\) | \(24020916664062500000\) | \([2]\) | \(645120\) | \(2.8094\) | |
| 11830.t2 | 11830t2 | \([1, -1, 1, -1203312, -430495789]\) | \(39920686684059609/6492304000000\) | \(31337111377936000000\) | \([2, 2]\) | \(322560\) | \(2.4629\) | |
| 11830.t3 | 11830t1 | \([1, -1, 1, -338032, 69289939]\) | \(884984855328729/83492864000\) | \(403004107390976000\) | \([4]\) | \(161280\) | \(2.1163\) | \(\Gamma_0(N)\)-optimal |
| 11830.t4 | 11830t4 | \([1, -1, 1, 2176688, -2415231789]\) | \(236293804275620391/658593925444000\) | \(-3178907086678428196000\) | \([2]\) | \(645120\) | \(2.8094\) |
Rank
sage: E.rank()
The elliptic curves in class 11830.t have rank \(1\).
Complex multiplication
The elliptic curves in class 11830.t do not have complex multiplication.Modular form 11830.2.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 LMFDB 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 LMFDB labels.
