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SageMath
E = EllipticCurve("jh1")
E.isogeny_class()
Elliptic curves in class 145200.jh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145200.jh1 | 145200u4 | \([0, 1, 0, -40076208, 97320021588]\) | \(502270291349/1889568\) | \(26779879805184000000000\) | \([2]\) | \(13440000\) | \(3.1628\) | |
| 145200.jh2 | 145200u2 | \([0, 1, 0, -2566208, -1582958412]\) | \(131872229/18\) | \(255104784000000000\) | \([2]\) | \(2688000\) | \(2.3581\) | |
| 145200.jh3 | 145200u3 | \([0, 1, 0, -1356208, 2920661588]\) | \(-19465109/248832\) | \(-3526568534016000000000\) | \([2]\) | \(6720000\) | \(2.8163\) | |
| 145200.jh4 | 145200u1 | \([0, 1, 0, -146208, -29318412]\) | \(-24389/12\) | \(-170069856000000000\) | \([2]\) | \(1344000\) | \(2.0115\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 145200.jh have rank \(1\).
Complex multiplication
The elliptic curves in class 145200.jh do not have complex multiplication.Modular form 145200.2.a.jh
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
