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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 38148.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38148.f1 | 38148d2 | \([0, -1, 0, -9390573, -11073296727]\) | \(-14820625871872000/529675443\) | \(-3272979853572625152\) | \([]\) | \(995328\) | \(2.6418\) | |
| 38148.f2 | 38148d1 | \([0, -1, 0, -26973, -37732311]\) | \(-351232000/99379467\) | \(-614087357925305088\) | \([]\) | \(331776\) | \(2.0924\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38148.f have rank \(1\).
Complex multiplication
The elliptic curves in class 38148.f do not have complex multiplication.Modular form 38148.2.a.f
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.
