Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 7260.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7260.l1 | 7260n4 | \([0, 1, 0, -30249556, 64026275300]\) | \(6749703004355978704/5671875\) | \(2572306572000000\) | \([2]\) | \(207360\) | \(2.6925\) | |
7260.l2 | 7260n3 | \([0, 1, 0, -1890181, 1000400300]\) | \(-26348629355659264/24169921875\) | \(-685095855468750000\) | \([2]\) | \(103680\) | \(2.3459\) | |
7260.l3 | 7260n2 | \([0, 1, 0, -381916, 83523284]\) | \(13584145739344/1195803675\) | \(542320423497388800\) | \([2]\) | \(69120\) | \(2.1432\) | |
7260.l4 | 7260n1 | \([0, 1, 0, 26459, 6095384]\) | \(72268906496/606436875\) | \(-17189438667390000\) | \([2]\) | \(34560\) | \(1.7966\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7260.l have rank \(0\).
Complex multiplication
The elliptic curves in class 7260.l do not have complex multiplication.Modular form 7260.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.