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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 7220.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7220.c1 | 7220g2 | \([0, 1, 0, -180620, -29589980]\) | \(7888624/5\) | \(413040253157120\) | \([2]\) | \(36480\) | \(1.7457\) | |
7220.c2 | 7220g1 | \([0, 1, 0, -9145, -645000]\) | \(-16384/25\) | \(-129075079111600\) | \([2]\) | \(18240\) | \(1.3992\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7220.c have rank \(1\).
Complex multiplication
The elliptic curves in class 7220.c do not have complex multiplication.Modular form 7220.2.a.c
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.