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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 2275.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2275.b1 | 2275f2 | \([1, 0, 0, -10388, 114517]\) | \(63473450669/33787663\) | \(65991529296875\) | \([2]\) | \(6720\) | \(1.3431\) | |
2275.b2 | 2275f1 | \([1, 0, 0, -6013, -178608]\) | \(12310389629/107653\) | \(210259765625\) | \([2]\) | \(3360\) | \(0.99651\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2275.b have rank \(0\).
Complex multiplication
The elliptic curves in class 2275.b do not have complex multiplication.Modular form 2275.2.a.b
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.