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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3075.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3075.b1 | 3075l1 | \([0, 1, 1, -16198, 788134]\) | \(-18801595227320320/588305187\) | \(-14707629675\) | \([5]\) | \(5400\) | \(1.0473\) | \(\Gamma_0(N)\)-optimal |
| 3075.b2 | 3075l2 | \([0, 1, 1, 74792, 2979994]\) | \(4737871769600/3128117427\) | \(-30548021748046875\) | \([]\) | \(27000\) | \(1.8520\) |
Rank
sage: E.rank()
The elliptic curves in class 3075.b have rank \(1\).
Complex multiplication
The elliptic curves in class 3075.b do not have complex multiplication.Modular form 3075.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
