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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 183872bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 183872.h2 | 183872bl1 | \([0, 1, 0, -5633, -120353]\) | \(62500/17\) | \(5377605828608\) | \([2]\) | \(245760\) | \(1.1506\) | \(\Gamma_0(N)\)-optimal |
| 183872.h1 | 183872bl2 | \([0, 1, 0, -32673, 2167231]\) | \(6097250/289\) | \(182838598172672\) | \([2]\) | \(491520\) | \(1.4972\) |
Rank
sage: E.rank()
The elliptic curves in class 183872bl have rank \(1\).
Complex multiplication
The elliptic curves in class 183872bl do not have complex multiplication.Modular form 183872.2.a.bl
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 Cremona 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 Cremona labels.
