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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 2496u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2496.b4 | 2496u1 | \([0, -1, 0, -1249, -354431]\) | \(-822656953/207028224\) | \(-54271206752256\) | \([2]\) | \(7680\) | \(1.3147\) | \(\Gamma_0(N)\)-optimal |
| 2496.b3 | 2496u2 | \([0, -1, 0, -83169, -9119871]\) | \(242702053576633/2554695936\) | \(669698211446784\) | \([2, 2]\) | \(15360\) | \(1.6612\) | |
| 2496.b1 | 2496u3 | \([0, -1, 0, -1327329, -588151935]\) | \(986551739719628473/111045168\) | \(29109824520192\) | \([2]\) | \(30720\) | \(2.0078\) | |
| 2496.b2 | 2496u4 | \([0, -1, 0, -149729, 7613313]\) | \(1416134368422073/725251155408\) | \(190120238883274752\) | \([2]\) | \(30720\) | \(2.0078\) |
Rank
sage: E.rank()
The elliptic curves in class 2496u have rank \(0\).
Complex multiplication
The elliptic curves in class 2496u do not have complex multiplication.Modular form 2496.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
