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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 158025r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 158025.l4 | 158025r1 | \([1, 1, 1, 1812, -269844]\) | \(357911/17415\) | \(-32013395859375\) | \([2]\) | \(405504\) | \(1.2712\) | \(\Gamma_0(N)\)-optimal |
| 158025.l3 | 158025r2 | \([1, 1, 1, -53313, -4569594]\) | \(9116230969/416025\) | \(764764456640625\) | \([2, 2]\) | \(811008\) | \(1.6177\) | |
| 158025.l2 | 158025r3 | \([1, 1, 1, -145188, 15275406]\) | \(184122897769/51282015\) | \(94269965355234375\) | \([2]\) | \(1622016\) | \(1.9643\) | |
| 158025.l1 | 158025r4 | \([1, 1, 1, -843438, -298496094]\) | \(36097320816649/80625\) | \(148210166015625\) | \([2]\) | \(1622016\) | \(1.9643\) |
Rank
sage: E.rank()
The elliptic curves in class 158025r have rank \(0\).
Complex multiplication
The elliptic curves in class 158025r do not have complex multiplication.Modular form 158025.2.a.r
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.
