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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 355740.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
355740.bn1 | 355740bn2 | \([0, -1, 0, -8592285060, -306515643083208]\) | \(1314817350433665559504/190690249278375\) | \(10174493597277089847878496000\) | \([2]\) | \(464486400\) | \(4.3891\) | |
355740.bn2 | 355740bn1 | \([0, -1, 0, -488083185, -5697394525458]\) | \(-3856034557002072064/1973796785296875\) | \(-6582134780857465727262750000\) | \([2]\) | \(232243200\) | \(4.0425\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 355740.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 355740.bn do not have complex multiplication.Modular form 355740.2.a.bn
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.