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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 259182.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259182.l1 | 259182l2 | \([1, -1, 0, -7596, -612144]\) | \(-549538142857/1528561664\) | \(-134832895819776\) | \([]\) | \(1088640\) | \(1.3985\) | |
259182.l2 | 259182l1 | \([1, -1, 0, 819, 18981]\) | \(688278503/2201024\) | \(-194150126016\) | \([]\) | \(362880\) | \(0.84919\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259182.l have rank \(2\).
Complex multiplication
The elliptic curves in class 259182.l do not have complex multiplication.Modular form 259182.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.