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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 19074.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19074.l1 | 19074r1 | \([1, 1, 1, -56650, -5210089]\) | \(832972004929/610368\) | \(14732799715392\) | \([2]\) | \(110592\) | \(1.4610\) | \(\Gamma_0(N)\)-optimal |
19074.l2 | 19074r2 | \([1, 1, 1, -45090, -7383369]\) | \(-420021471169/727634952\) | \(-17563338860711688\) | \([2]\) | \(221184\) | \(1.8075\) |
Rank
sage: E.rank()
The elliptic curves in class 19074.l have rank \(0\).
Complex multiplication
The elliptic curves in class 19074.l do not have complex multiplication.Modular form 19074.2.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.