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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 3150.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.bc1 | 3150v2 | \([1, -1, 1, -515, -4373]\) | \(-30642435/56\) | \(-27556200\) | \([]\) | \(864\) | \(0.31923\) | |
| 3150.bc2 | 3150v1 | \([1, -1, 1, 10, -33]\) | \(179685/686\) | \(-463050\) | \([]\) | \(288\) | \(-0.23008\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3150.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 3150.bc do not have complex multiplication.Modular form 3150.2.a.bc
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.
