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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 456304bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 456304.bd3 | 456304bd1 | \([0, 1, 0, -268704, 53520884]\) | \(11134383337/316\) | \(60893177430016\) | \([]\) | \(2280960\) | \(1.7466\) | \(\Gamma_0(N)\)-optimal |
| 456304.bd2 | 456304bd2 | \([0, 1, 0, -470864, -37451116]\) | \(59914169497/31554496\) | \(6080549125451677696\) | \([]\) | \(6842880\) | \(2.2959\) | |
| 456304.bd1 | 456304bd3 | \([0, 1, 0, -30130624, -63669043916]\) | \(15698803397448457/20709376\) | \(3990695276053528576\) | \([]\) | \(20528640\) | \(2.8452\) |
Rank
sage: E.rank()
The elliptic curves in class 456304bd have rank \(0\).
Complex multiplication
The elliptic curves in class 456304bd do not have complex multiplication.Modular form 456304.2.a.bd
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
