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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 11011.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11011.f1 | 11011c3 | \([0, 1, 1, -14197, 1600022]\) | \(-178643795968/524596891\) | \(-929355392816851\) | \([]\) | \(51840\) | \(1.5591\) | |
| 11011.f2 | 11011c1 | \([0, 1, 1, -887, -10488]\) | \(-43614208/91\) | \(-161212051\) | \([]\) | \(5760\) | \(0.46044\) | \(\Gamma_0(N)\)-optimal |
| 11011.f3 | 11011c2 | \([0, 1, 1, 1533, -50055]\) | \(224755712/753571\) | \(-1334996994331\) | \([]\) | \(17280\) | \(1.0097\) |
Rank
sage: E.rank()
The elliptic curves in class 11011.f have rank \(0\).
Complex multiplication
The elliptic curves in class 11011.f do not have complex multiplication.Modular form 11011.2.a.f
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
