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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 9075.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9075.k1 | 9075e2 | \([0, -1, 1, -18123783, -29691617407]\) | \(-196566176333824/421875\) | \(-1413010201904296875\) | \([]\) | \(342144\) | \(2.7302\) | |
| 9075.k2 | 9075e1 | \([0, -1, 1, -155283, -66053032]\) | \(-123633664/492075\) | \(-1648135099501171875\) | \([]\) | \(114048\) | \(2.1809\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9075.k have rank \(0\).
Complex multiplication
The elliptic curves in class 9075.k do not have complex multiplication.Modular form 9075.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
