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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 18480.cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18480.cd1 | 18480cs2 | \([0, 1, 0, -516, -4680]\) | \(59466754384/121275\) | \(31046400\) | \([2]\) | \(7680\) | \(0.32407\) | |
18480.cd2 | 18480cs1 | \([0, 1, 0, -21, -126]\) | \(-67108864/343035\) | \(-5488560\) | \([2]\) | \(3840\) | \(-0.022504\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18480.cd have rank \(0\).
Complex multiplication
The elliptic curves in class 18480.cd do not have complex multiplication.Modular form 18480.2.a.cd
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.