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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 37485.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37485.n1 | 37485x4 | \([1, -1, 1, -1406138, -641385034]\) | \(3585019225176649/316207395\) | \(27119881700664795\) | \([2]\) | \(589824\) | \(2.1941\) | |
| 37485.n2 | 37485x3 | \([1, -1, 1, -510908, 133538402]\) | \(171963096231529/9865918125\) | \(846161527684843125\) | \([2]\) | \(589824\) | \(2.1941\) | |
| 37485.n3 | 37485x2 | \([1, -1, 1, -94163, -8488294]\) | \(1076575468249/258084225\) | \(22134882869541225\) | \([2, 2]\) | \(294912\) | \(1.8475\) | |
| 37485.n4 | 37485x1 | \([1, -1, 1, 13882, -838708]\) | \(3449795831/5510295\) | \(-472596627715695\) | \([2]\) | \(147456\) | \(1.5009\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37485.n have rank \(1\).
Complex multiplication
The elliptic curves in class 37485.n do not have complex multiplication.Modular form 37485.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
