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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 62790.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62790.l1 | 62790i2 | \([1, 0, 1, -41569, -3265474]\) | \(7943601056572322569/205785748350\) | \(205785748350\) | \([2]\) | \(190464\) | \(1.2774\) | |
62790.l2 | 62790i1 | \([1, 0, 1, -2699, -47038]\) | \(2173206713502889/310938466020\) | \(310938466020\) | \([2]\) | \(95232\) | \(0.93085\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62790.l have rank \(0\).
Complex multiplication
The elliptic curves in class 62790.l do not have complex multiplication.Modular form 62790.2.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.