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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 47190.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47190.ci1 | 47190cq4 | \([1, 0, 0, -10469951, -13040497095]\) | \(71647584155243142409/10140000\) | \(17963628540000\) | \([2]\) | \(1843200\) | \(2.3962\) | |
| 47190.ci2 | 47190cq3 | \([1, 0, 0, -751231, -139542919]\) | \(26465989780414729/10571870144160\) | \(18728712844458233760\) | \([2]\) | \(1843200\) | \(2.3962\) | |
| 47190.ci3 | 47190cq2 | \([1, 0, 0, -654431, -203760039]\) | \(17496824387403529/6580454400\) | \(11657676377318400\) | \([2, 2]\) | \(921600\) | \(2.0496\) | |
| 47190.ci4 | 47190cq1 | \([1, 0, 0, -34911, -4150695]\) | \(-2656166199049/2658140160\) | \(-4709057439989760\) | \([2]\) | \(460800\) | \(1.7031\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47190.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 47190.ci do not have complex multiplication.Modular form 47190.2.a.ci
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.
