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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 44352.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44352.a1 | 44352bd2 | \([0, 0, 0, -270252, -54075600]\) | \(11422548526761/4312\) | \(824036032512\) | \([2]\) | \(294912\) | \(1.6370\) | |
| 44352.a2 | 44352bd1 | \([0, 0, 0, -16812, -853200]\) | \(-2749884201/54208\) | \(-10359310123008\) | \([2]\) | \(147456\) | \(1.2905\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44352.a have rank \(0\).
Complex multiplication
The elliptic curves in class 44352.a do not have complex multiplication.Modular form 44352.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
