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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 57330e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57330.b2 | 57330e1 | \([1, -1, 0, -298860, -18710784]\) | \(2709453996621/1428050000\) | \(1555928148861450000\) | \([2]\) | \(1146880\) | \(2.1823\) | \(\Gamma_0(N)\)-optimal |
57330.b1 | 57330e2 | \([1, -1, 0, -3776880, -2821299300]\) | \(5468613271737741/6601562500\) | \(7192715185195312500\) | \([2]\) | \(2293760\) | \(2.5289\) |
Rank
sage: E.rank()
The elliptic curves in class 57330e have rank \(0\).
Complex multiplication
The elliptic curves in class 57330e do not have complex multiplication.Modular form 57330.2.a.e
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 Cremona 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 Cremona labels.