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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 25230.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25230.q1 | 25230r3 | \([1, 1, 1, -141690436, 641054266949]\) | \(21685195471991381/309586821120\) | \(4491221206193083939553280\) | \([2]\) | \(6496000\) | \(3.5347\) | |
| 25230.q2 | 25230r4 | \([1, 1, 1, -16818756, 1731533674053]\) | \(-36267977929301/89261680665600\) | \(-1294932231467262761458406400\) | \([2]\) | \(12992000\) | \(3.8813\) | |
| 25230.q3 | 25230r1 | \([1, 1, 1, -14257911, -20727590211]\) | \(22095784790981/450000\) | \(6528215689141050000\) | \([2]\) | \(1299200\) | \(2.7300\) | \(\Gamma_0(N)\)-optimal |
| 25230.q4 | 25230r2 | \([1, 1, 1, -13770131, -22211026747]\) | \(-19904714311301/3164062500\) | \(-45901516564273007812500\) | \([2]\) | \(2598400\) | \(3.0766\) |
Rank
sage: E.rank()
The elliptic curves in class 25230.q have rank \(1\).
Complex multiplication
The elliptic curves in class 25230.q do not have complex multiplication.Modular form 25230.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
