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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 373635bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 373635.bv4 | 373635bv1 | \([1, -1, 0, 1483101, 437279080]\) | \(10519294081031/8500170375\) | \(-291525644873700048375\) | \([2]\) | \(16588800\) | \(2.6147\) | \(\Gamma_0(N)\)-optimal |
| 373635.bv3 | 373635bv2 | \([1, -1, 0, -7110504, 3811128403]\) | \(1159246431432649/488076890625\) | \(16739303332776255140625\) | \([2, 2]\) | \(33177600\) | \(2.9612\) | |
| 373635.bv1 | 373635bv3 | \([1, -1, 0, -97903809, 372740643940]\) | \(3026030815665395929/1364501953125\) | \(46797569256509033203125\) | \([2]\) | \(66355200\) | \(3.3078\) | |
| 373635.bv2 | 373635bv4 | \([1, -1, 0, -53814879, -149295153722]\) | \(502552788401502649/10024505152875\) | \(343804912172906118190875\) | \([2]\) | \(66355200\) | \(3.3078\) |
Rank
sage: E.rank()
The elliptic curves in class 373635bv have rank \(1\).
Complex multiplication
The elliptic curves in class 373635bv do not have complex multiplication.Modular form 373635.2.a.bv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
