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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 7530l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7530.l2 | 7530l1 | \([1, 0, 0, -348930, 79128900]\) | \(4698278114490760338721/12005252190000000\) | \(12005252190000000\) | \([7]\) | \(122304\) | \(1.9617\) | \(\Gamma_0(N)\)-optimal |
7530.l1 | 7530l2 | \([1, 0, 0, -47482380, -125939016990]\) | \(11839167111346898373312419521/5648830713399532590\) | \(5648830713399532590\) | \([]\) | \(856128\) | \(2.9347\) |
Rank
sage: E.rank()
The elliptic curves in class 7530l have rank \(0\).
Complex multiplication
The elliptic curves in class 7530l do not have complex multiplication.Modular form 7530.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.