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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 140790.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
140790.l1 | 140790ck2 | \([1, 1, 0, -1355562, -98908596]\) | \(5855456577737521/3299765625000\) | \(155240380921640625000\) | \([2]\) | \(5529600\) | \(2.5644\) | |
140790.l2 | 140790ck1 | \([1, 1, 0, 333918, -12069324]\) | \(87522470053199/52018200000\) | \(-2447242047034200000\) | \([2]\) | \(2764800\) | \(2.2178\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 140790.l have rank \(1\).
Complex multiplication
The elliptic curves in class 140790.l do not have complex multiplication.Modular form 140790.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.