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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 94815b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94815.bg2 | 94815b1 | \([1, -1, 0, -3390, 4031]\) | \(1860867/1075\) | \(2489361662025\) | \([2]\) | \(110592\) | \(1.0681\) | \(\Gamma_0(N)\)-optimal |
94815.bg1 | 94815b2 | \([1, -1, 0, -36465, -2661814]\) | \(2315685267/9245\) | \(21408510293415\) | \([2]\) | \(221184\) | \(1.4147\) |
Rank
sage: E.rank()
The elliptic curves in class 94815b have rank \(2\).
Complex multiplication
The elliptic curves in class 94815b do not have complex multiplication.Modular form 94815.2.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 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.