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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 53361.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53361.bi1 | 53361ba1 | \([0, 0, 1, -4766916, -4005962942]\) | \(-78843215872/539\) | \(-81895614230750859\) | \([]\) | \(1152000\) | \(2.4262\) | \(\Gamma_0(N)\)-optimal |
53361.bi2 | 53361ba2 | \([0, 0, 1, -2632476, -7601160317]\) | \(-13278380032/156590819\) | \(-23792395741931970307539\) | \([]\) | \(3456000\) | \(2.9755\) | |
53361.bi3 | 53361ba3 | \([0, 0, 1, 23514414, 196749858478]\) | \(9463555063808/115539436859\) | \(-17555052225311429925028779\) | \([]\) | \(10368000\) | \(3.5248\) |
Rank
sage: E.rank()
The elliptic curves in class 53361.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 53361.bi do not have complex multiplication.Modular form 53361.2.a.bi
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.