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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 3150.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.bh1 | 3150y1 | \([1, -1, 1, -128105, 17641897]\) | \(551105805571803/1376829440\) | \(580849920000000\) | \([2]\) | \(26880\) | \(1.7103\) | \(\Gamma_0(N)\)-optimal |
| 3150.bh2 | 3150y2 | \([1, -1, 1, -80105, 30985897]\) | \(-134745327251163/903920796800\) | \(-381341586150000000\) | \([2]\) | \(53760\) | \(2.0569\) |
Rank
sage: E.rank()
The elliptic curves in class 3150.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 3150.bh do not have complex multiplication.Modular form 3150.2.a.bh
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.
