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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 116610.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116610.v1 | 116610o4 | \([1, 1, 0, -29444197, -61502964791]\) | \(584874606003693846049/59671196032500\) | \(288021466050435292500\) | \([2]\) | \(11010048\) | \(2.9590\) | |
| 116610.v2 | 116610o3 | \([1, 1, 0, -11077277, 13523829441]\) | \(31143162165402407329/1642456054687500\) | \(7927821666870117187500\) | \([4]\) | \(11010048\) | \(2.9590\) | |
| 116610.v3 | 116610o2 | \([1, 1, 0, -1981697, -805347291]\) | \(178309998550446049/45259256250000\) | \(218457785400806250000\) | \([2, 2]\) | \(5505024\) | \(2.6124\) | |
| 116610.v4 | 116610o1 | \([1, 1, 0, 303183, -80126379]\) | \(638522048185631/945940320000\) | \(-4565873250038880000\) | \([2]\) | \(2752512\) | \(2.2659\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116610.v have rank \(0\).
Complex multiplication
The elliptic curves in class 116610.v do not have complex multiplication.Modular form 116610.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
