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SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 343728.fj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 343728.fj1 | 343728fj2 | \([0, 0, 0, -537843, -956763470]\) | \(-5762391987245041/129101095135628\) | \(-385493804457463037952\) | \([]\) | \(14400000\) | \(2.6309\) | |
| 343728.fj2 | 343728fj1 | \([0, 0, 0, -74163, 10049650]\) | \(-15107691357361/5868735488\) | \(-17523950267400192\) | \([]\) | \(2880000\) | \(1.8262\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 343728.fj have rank \(0\).
Complex multiplication
The elliptic curves in class 343728.fj do not have complex multiplication.Modular form 343728.2.a.fj
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
