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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 25230u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25230.s3 | 25230u1 | \([1, 1, 1, -48375, 1468617]\) | \(21047437081/10570500\) | \(6287579914630500\) | \([2]\) | \(241920\) | \(1.7242\) | \(\Gamma_0(N)\)-optimal |
| 25230.s4 | 25230u2 | \([1, 1, 1, 178695, 11550525]\) | \(1060895910599/709593750\) | \(-422082910935843750\) | \([2]\) | \(483840\) | \(2.0707\) | |
| 25230.s1 | 25230u3 | \([1, 1, 1, -2129850, -1197233913]\) | \(1796316223281481/70240320\) | \(41780580410502720\) | \([2]\) | \(725760\) | \(2.2735\) | |
| 25230.s2 | 25230u4 | \([1, 1, 1, -2028930, -1315673625]\) | \(-1552876541267401/356893992600\) | \(-212288869923281424600\) | \([2]\) | \(1451520\) | \(2.6200\) |
Rank
sage: E.rank()
The elliptic curves in class 25230u have rank \(1\).
Complex multiplication
The elliptic curves in class 25230u do not have complex multiplication.Modular form 25230.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
