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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 23520bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23520.l3 | 23520bg1 | \([0, -1, 0, -3446, -75480]\) | \(601211584/11025\) | \(83013134400\) | \([2, 2]\) | \(36864\) | \(0.88997\) | \(\Gamma_0(N)\)-optimal |
| 23520.l4 | 23520bg2 | \([0, -1, 0, -16, -222284]\) | \(-8/354375\) | \(-21346234560000\) | \([2]\) | \(73728\) | \(1.2365\) | |
| 23520.l2 | 23520bg3 | \([0, -1, 0, -7121, 117825]\) | \(82881856/36015\) | \(17355279298560\) | \([2]\) | \(73728\) | \(1.2365\) | |
| 23520.l1 | 23520bg4 | \([0, -1, 0, -54896, -4932360]\) | \(303735479048/105\) | \(6324810240\) | \([2]\) | \(73728\) | \(1.2365\) |
Rank
sage: E.rank()
The elliptic curves in class 23520bg have rank \(1\).
Complex multiplication
The elliptic curves in class 23520bg do not have complex multiplication.Modular form 23520.2.a.bg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
