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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 72075.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72075.c1 | 72075m2 | \([0, -1, 1, -200208, 35409068]\) | \(-102400/3\) | \(-26001084404296875\) | \([]\) | \(913500\) | \(1.9286\) | |
72075.c2 | 72075m1 | \([0, -1, 1, 1602, -109492]\) | \(20480/243\) | \(-5391584862075\) | \([]\) | \(182700\) | \(1.1239\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72075.c have rank \(0\).
Complex multiplication
The elliptic curves in class 72075.c do not have complex multiplication.Modular form 72075.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.