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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 30015b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30015.c2 | 30015b1 | \([1, -1, 1, -60728, 6649962]\) | \(-33974761330806841/6424789539375\) | \(-4683671574204375\) | \([2]\) | \(264192\) | \(1.7310\) | \(\Gamma_0(N)\)-optimal |
| 30015.c1 | 30015b2 | \([1, -1, 1, -1012073, 392134956]\) | \(157264717208387436361/4368589453125\) | \(3184701711328125\) | \([2]\) | \(528384\) | \(2.0775\) |
Rank
sage: E.rank()
The elliptic curves in class 30015b have rank \(1\).
Complex multiplication
The elliptic curves in class 30015b do not have complex multiplication.Modular form 30015.2.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 Cremona 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 Cremona labels.
