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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 393008.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 393008.f1 | 393008f2 | \([0, 1, 0, -4327968, 3464003860]\) | \(2471097448795250/98942809\) | \(358980037949130752\) | \([2]\) | \(8847360\) | \(2.4514\) | |
| 393008.f2 | 393008f1 | \([0, 1, 0, -257528, 59487844]\) | \(-1041220466500/242597383\) | \(-440090687923059712\) | \([2]\) | \(4423680\) | \(2.1049\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 393008.f have rank \(2\).
Complex multiplication
The elliptic curves in class 393008.f do not have complex multiplication.Modular form 393008.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
